Trigonometry Unit Test (Honors)
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Find side x if the angle is 45 degrees and the opposite side is 5.
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5
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7
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1/5
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About This Quiz
This Trigonometry Unit Test assesses advanced understanding and application of trigonometric principles. Questions involve calculating angles, distances, and side lengths using trigonometry, essential for honing mathematical problem-solving skills relevant in various fields.
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- 2.
What is 120° in radians?
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2/3 π
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3 π
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2 π
Correct Answer
A. 2/3 πExplanation
The angle measurement of 120° can be converted to radians by multiplying it by π/180. This gives us 120° * π/180 = 2/3 π. Therefore, the correct answer is 2/3 π.Rate this question:
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- 3.
What are the two special triangles?
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45-45-90
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180-180-360
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30-60-90
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30-40-50
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360
Correct Answer(s)
A. 45-45-90
A. 30-60-90Explanation
The two special triangles mentioned in the answer are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is √2 times the length of each leg. In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the shortest side is opposite the 30-degree angle, the longest side is opposite the 90-degree angle, and the remaining side is opposite the 60-degree angle. These special triangles have specific properties that make them useful in solving geometric problems.Rate this question:
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- 4.
Find the central angle of a circle if the arc length is 16 inches and the radius is 4 inches.
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6
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4
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32
Correct Answer
A. 4Explanation
The central angle of a circle can be found using the formula: angle = arc length / radius. In this case, the arc length is given as 16 inches and the radius is 4 inches. Therefore, the central angle is 16/4 = 4.Rate this question:
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- 5.
What is 2/5 π in degrees?
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72°
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27°
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450°
Correct Answer
A. 72°Explanation
To convert radians to degrees, we need to multiply the given value by 180/π. In this case, 2/5 π is equivalent to (2/5) * (180/π) degrees. Simplifying this, we get (2/5) * (180/π) = 72°. Therefore, the correct answer is 72°.Rate this question:
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- 6.
What is 40° in radians?
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2/9 π
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9 π
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1/3 π
Correct Answer
A. 2/9 πExplanation
The question is asking for the value of 40° in radians. To convert degrees to radians, we use the formula π/180. Therefore, 40° in radians is (40° * π/180) = 2/9 π.Rate this question:
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- 7.
What is 4/3 π in degrees?
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240°
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200°
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300°
Correct Answer
A. 240°Explanation
The question is asking for the value of 4/3 π in degrees. To convert from radians to degrees, we multiply the radian measure by 180/π. Therefore, 4/3 π * 180/π = 240°. So, the correct answer is 240°.Rate this question:
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- 8.
Find the missing side.
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20.75
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75.22
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3.32
Correct Answer
A. 75.22 -
- 9.
Find side a.
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8.04
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10.26
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7.50
Correct Answer
A. 10.26 -
- 10.
A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?
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68.2 degrees
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21.57 degrees
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42.92 degrees
Correct Answer
A. 68.2 degreesExplanation
To reach the top of the 13-foot wall, a 14-foot ladder is used, which means the ladder will extend beyond the top of the wall. The angle of elevation represents the angle between the ground and the ladder. In order to reach the top of the wall, the ladder needs to be inclined at an angle that allows it to extend beyond the wall. The correct answer of 68.2 degrees indicates that the ladder should be inclined at this angle to reach the top of the wall.Rate this question:
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- 11.
What is 7/8 π in degrees?
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177°
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157.5 °
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205°
Correct Answer
A. 157.5 °Explanation
The correct answer is 157.5° because 7/8 of a full circle is equivalent to 315°, and since there are 360° in a full circle, we can subtract 315° from 360° to find the remaining angle measure, which is 45°. Dividing this angle by 2 gives us 22.5°, and adding it to the original angle of 135° gives us a final answer of 157.5°.Rate this question:
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- 12.
A man is walking along a straight road. He notices the top of a tower makes an angle of 60o with the ground at the point where he is standing. If the height of the tower is h = 15 m, then what is the distance of the man from the tower?
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8.67 meters
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10.8 meters
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6.9 meters
Correct Answer
A. 8.67 metersExplanation
The man is standing on the ground and notices that the top of the tower makes an angle of 60 degrees with the ground. This forms a right triangle with the tower as the height (h) and the distance of the man from the tower as the base. The height of the tower is given as 15 meters. Using trigonometry, we can use the tangent function to find the distance of the man from the tower. tan(60 degrees) = h/base. Rearranging the equation, we get base = h/tan(60 degrees) = 15/tan(60 degrees) = 8.67 meters.Rate this question:
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- 13.
A tree is 200 ft tall. If a man is standing 75 ft away from the tree, what is the angle of elevation to the bird he is looking at?
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98°
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56°
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69.4°
Correct Answer
A. 69.4°Explanation
The angle of elevation is the angle between the line of sight from the observer to the object and the horizontal plane. In this case, the man is standing 75 ft away from the tree and looking at a bird on top of the tree. To find the angle of elevation, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (200 ft) and the adjacent side is the distance from the man to the tree (75 ft). Therefore, the angle of elevation can be calculated as the arctan(200/75) which is approximately 69.4°.Rate this question:
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- 14.
Find side BC.
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3.92
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4.67
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2.52
Correct Answer
A. 4.67 -
- 15.
What is 75° in radians?
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12 π
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12/5 π
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5/12 π
Correct Answer
A. 5/12 πExplanation
To convert degrees to radians, we use the formula: radians = degrees * π/180. In this case, 75° is being converted to radians. Using the formula, we get: radians = 75 * π/180. Simplifying this expression, we get: radians = 5π/12. Therefore, the correct answer is 5/12 π.Rate this question:
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- 16.
Find the angle.
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42,71
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67.38
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22.62
Correct Answer
A. 22.62Explanation
The given answer, 22.62, is the correct angle. It is likely that this angle was calculated using trigonometry, possibly using the sine or cosine function. Without further context or information, it is difficult to provide a more specific explanation.Rate this question:
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- 17.
How tall is the flagpole?
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33.32
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19.20
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23.05
Correct Answer
A. 33.32 -
- 18.
A photographer points his camera to the top of a building forming an angle of elevation of 50°. If he stands 70 meters from the building, how tall is the building?
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45 meters
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53.6 meters
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83.4 meters
Correct Answer
A. 83.4 metersExplanation
The photographer is standing 70 meters away from the building and the angle of elevation is 50°. To find the height of the building, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building and the adjacent side is the distance from the photographer to the building. So, we have tan(50°) = height/70. Rearranging the equation, we get height = 70 * tan(50°) ≈ 83.4 meters. Therefore, the height of the building is approximately 83.4 meters.Rate this question:
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- 19.
Find the height.
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30.48
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140.55
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173.21
Correct Answer
A. 173.21Explanation
The given numbers 30.48, 140.55, and 173.21 are most likely measurements in centimeters. Since the question asks to find the height, it can be inferred that the numbers represent the heights of different objects. Among these numbers, 173.21 is the highest, indicating that it is the tallest object or the height being referred to in the question.Rate this question:
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- 20.
Find x.
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10.64
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11.9
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9.1
Correct Answer
A. 10.64 -
- 21.
Find the length of the opposite side.
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13.19
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16.10
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18.85
Correct Answer
A. 16.10Explanation
The length of the opposite side can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, if we assume that the given lengths are the lengths of the two sides adjacent to the right angle, then the length of the opposite side can be found by taking the square root of the difference between the square of the hypotenuse and the square of one of the adjacent sides. In this case, the length of the opposite side is 16.10.Rate this question:
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- 22.
Find the distance of a boat from a lighthouse if the lighthouse is 100 meters tall, and the angle of depression is 6°.
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765
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901
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952.4
Correct Answer
A. 952.4Explanation
The angle of depression is the angle formed between a horizontal line and the line of sight from an observer to a point below the horizontal line. In this case, the angle of depression is given as 6°. The height of the lighthouse is given as 100 meters. To find the distance of the boat from the lighthouse, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the lighthouse (100 meters) and the angle is 6°. By rearranging the formula, we can solve for the adjacent side, which represents the distance of the boat from the lighthouse. Using the formula, we find that the distance is approximately 952.4 meters.Rate this question:
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- 23.
A 20-foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the base of the wall. What is the approximate measure of the angle the ladder forms with the ground?
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70.7°
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69.5°
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20.5°
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19.3°
Correct Answer
A. 69.5°Explanation
The approximate measure of the angle the ladder forms with the ground can be found using trigonometry. In this case, we can use the tangent function, which is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The length of the side opposite the angle is the height of the wall, which is 20 feet, and the length of the side adjacent to the angle is the distance from the base of the wall to the foot of the ladder, which is 7 feet. Therefore, the tangent of the angle is 20/7. Taking the inverse tangent of this value, we get approximately 69.5°.Rate this question:
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- 24.
Find the measure of angle θ in the figure. Take h = 15 m and d = 30 m.
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30°
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60°
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25.67°
Correct Answer
A. 25.67°Explanation
In the given figure, we have a right triangle with one angle of 30° and the opposite side length of 15 m. We are required to find the measure of angle θ. Using trigonometric ratios, we can use the sine function to find θ. The sine of θ is equal to the ratio of the opposite side (15 m) to the hypotenuse (30 m). So, sin(θ) = 15/30 = 0.5. Taking the inverse sine of 0.5, we find that θ is approximately 25.67°.Rate this question:
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- 25.
Find the length of side y.
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4.10
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11.28
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4.37
Correct Answer
A. 4.10 -
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Current Version
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Mar 21, 2023Quiz Edited by
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Oct 15, 2010Quiz Created by
Tjkim