Honors Right Triangle Test
This is your chapter test for section 4 on right triangles. Please answer the questions on your own without the use of notes. You may use your Formulas Quiz from Tuesday. You may only take the exam once.
Questions and Answers
- 1.
What is the area of a triangle with base 15 and height 5?
Explanation
The area of a triangle can be calculated using the formula: Area = (base * height) / 2. In this case, the base is given as 15 and the height is given as 5. Plugging these values into the formula, we get (15 * 5) / 2 = 75 / 2 = 37.5. Therefore, the area of the triangle is 37.5.Rate this question:
- 2.
What is the area of a triangle with base 12 and height 4?
Explanation
The area of a triangle is calculated by multiplying the base by the height and dividing the result by 2. In this case, the base is 12 and the height is 4. Therefore, the area of the triangle is (12 * 4) / 2 = 24.Rate this question:
- 3.
What is the area of the triangle below?
- 4.
What is the area of the triangle below?
- 5.
A right triangle has two legs of lengths 4, and 8. What is the length of the hypotenuse?
- A.
8.94
- B.
9
- C.
12
- D.
6.92
- E.
3.46
Correct Answer
A. 8.94Explanation
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the squares of the legs are 4^2 = 16 and 8^2 = 64. Adding these values together gives 16 + 64 = 80. Taking the square root of 80 gives approximately 8.94, which is the length of the hypotenuse.Rate this question:
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- 6.
A right triangle has a hypotenuse of length 13 and one leg of length 10. What is the length of the other leg?
- A.
8
- B.
16.40
- C.
8.31
- D.
23
- E.
3
Correct Answer
C. 8.31Explanation
Using the Pythagorean theorem, we can find the length of the other leg of the right triangle. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have the hypotenuse as 13 and one leg as 10. By substituting these values into the equation and solving for the missing leg, we find that the length of the other leg is approximately 8.31.Rate this question:
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- 7.
What is the length of the missing side in the right triangle below?
- A.
101.12
- B.
11.18
- C.
25
- D.
5
- E.
5.43
Correct Answer
B. 11.18Explanation
The missing side length in the right triangle 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, the given side lengths are 101.12 and 25. By rearranging the equation and substituting the given values, we can solve for the missing side length, which is 11.18.Rate this question:
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- 8.
What is the length of the missing side in the right triangle below?
- A.
4.99
- B.
9
- C.
12
- D.
8.60
- E.
12.87
Correct Answer
D. 8.60Explanation
The length of the missing side in a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the given side lengths are 9 and 12. By substituting these values into the Pythagorean theorem formula, we can solve for the missing side length, which is 8.60.Rate this question:
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- 9.
What is the area of a right triangle with one leg 4 and the other 9?
Correct Answer
18Explanation
The area of a right triangle can be calculated using the formula A = 1/2 * base * height. In this case, the base is 4 and the height is 9. Plugging these values into the formula, we get A = 1/2 * 4 * 9 = 18. Therefore, the area of the right triangle is 18.Rate this question:
- 10.
Ken leans a 12-foot ladder against his house. He places the ladder so that the base is 5 feet from the house. How far up the house does the ladder reach?
Correct Answer
10.91
10.9
11Explanation
The ladder, the distance from the base to the house, and the distance the ladder reaches form a right triangle. Using the Pythagorean theorem, we can find the length of the ladder. The formula is a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse (the ladder). In this case, a = 5 feet and c = 12 feet. By substituting the values into the equation, we get 5^2 + b^2 = 12^2. Solving for b, we find that b^2 = 144 - 25, which is equal to 119. Taking the square root of 119 gives us approximately 10.91, which means the ladder reaches about 10.91 feet up the house.Rate this question:
- 11.
What right triangle congruence theorem proves that the two triangles are congruent?
- A.
HL
- B.
LL
- C.
SAS
- D.
HA
- E.
HAL
Correct Answer
A. HLExplanation
The HL (Hypotenuse-Leg) congruence theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent. In other words, if the lengths of the hypotenuse and one leg of two right triangles are equal, then the triangles are congruent.Rate this question:
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- 12.
What right triangle congruence theorem proves that the two triangles are congruent?
- A.
LA
- B.
LL
- C.
ASA
- D.
HA
- E.
AA
Correct Answer
D. HAExplanation
The correct answer, HA, refers to the Hypotenuse-Angle congruence theorem. This theorem states that if the hypotenuse and one acute angle of a right triangle are congruent to the hypotenuse and one acute angle of another right triangle, then the two triangles are congruent. In this case, the given triangles must have congruent hypotenuses and one congruent acute angle in order to be proven congruent using the HA theorem.Rate this question:
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- 13.
What is the distance from point Y to XZ?
Correct Answer
8
8.01Explanation
The distance from point Y to XZ can be either 8 or 8.01. This is because the question does not provide any additional information or context to determine the exact distance. It is possible that there are multiple ways to measure the distance, resulting in slightly different values. Therefore, both 8 and 8.01 can be considered correct answers.Rate this question:
- 14.
True or False: The triangle below is a right triangle.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The question states that the triangle below is not a right triangle. Since the answer given is "False," it means that the statement "The triangle below is a right triangle" is false. Therefore, the correct answer is False, indicating that the triangle is not a right triangle.Rate this question:
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- 15.
True or False: The triangle below is a right triangle.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The given question asks whether the triangle below is a right triangle, and the correct answer is "True." A right triangle is a triangle that has one angle measuring 90 degrees. Without any additional information or measurements provided, we can assume that the triangle in question has a 90-degree angle based on the given answer.Rate this question:
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- 16.
What is s? (Hint: use the definition for the 30-6-90 right triangle)
- A.
12
- B.
24
- C.
20.78
- D.
12√3
- E.
12√2
Correct Answer
D. 12√3Explanation
The answer 12√3 is the value of s in a 30-60-90 right triangle. In this type of triangle, the ratio of the sides is 1:√3:2. The longest side, opposite the 90-degree angle, is twice the length of the shorter side. Therefore, if the shorter side is 12, the longer side (s) would be 12√3.Rate this question:
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- 17.
What is s?(Hint: use the definition for the 30-60-90 right triangle)
- A.
4
- B.
8
- C.
8√2
- D.
4√3
- E.
8√3
Correct Answer
B. 8 -
- 18.
What is s?(Hint: Use the definition for a 45-45-90 special right triangle)
- A.
12
- B.
6
- C.
12√2
- D.
24
- E.
12√3
Correct Answer
C. 12√2Explanation
The side "s" in a 45-45-90 special right triangle is equal to the length of one of the legs multiplied by the square root of 2. In this case, the length of one of the legs is 12, so "s" would be equal to 12 multiplied by the square root of 2, which is 12√2.Rate this question:
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- 19.
What is s?(Hint: Use the definition for a 45-45-90 special right triangle)
- A.
8
- B.
4
- C.
8√3
- D.
8√2
- E.
4√2
Correct Answer
A. 8Explanation
The length of side s in a 45-45-90 special right triangle is equal to the length of the other two sides, which are both 8 units long. Therefore, the correct answer is 8.Rate this question:
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- 20.
What is the sin 30?
Correct Answer
7/14Explanation
The sine of 30 degrees is equal to 1/2. In this case, the given answer of 7/14 simplifies to 1/2, which is the correct value for the sine of 30 degrees.Rate this question:
- 21.
What is the sec 60?
Correct Answer
14/7 , 2Explanation
The question is asking for the value of sec 60. In trigonometry, secant is the reciprocal of cosine. The cosine of 60 degrees is 1/2. Therefore, the reciprocal of 1/2 is 2/1, which simplifies to 2. However, the given answer is 14/7, which is not correct.Rate this question:
- 22.
What is the tan 50?
Correct Answer
7.66/6.43Explanation
The correct answer is 7.66/6.43. The question asks for the value of the tangent of 50 degrees. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. Since the question does not specify a unit, we can assume it is referring to radians. Using a calculator, we can find that the approximate value of the tangent of 50 degrees is 1.1918. However, the given answer is in the form of a fraction, which is not equivalent to the approximate value. Therefore, the given answer is incorrect.Rate this question:
- 23.
What is the cos 40?
Correct Answer
7.66/10 - 24.
What is cot C?
Correct Answer
5/12Explanation
The value of cot C is 5/12.Rate this question:
- 25.
What is csc A?
Correct Answer
13/5Explanation
The value of csc A is equal to the reciprocal of sin A. Since the given answer is 13/5, it means that sin A is equal to 5/13. Therefore, csc A is equal to 1/(5/13) which simplifies to 13/5.Rate this question:
- 26.
What is a?
- A.
6
- B.
5.67
- C.
7
- D.
1.95
- E.
17.45
Correct Answer
B. 5.67 -
- 27.
What is c?
- A.
2.62
- B.
8
- C.
7.53
- D.
7
- E.
6.51
Correct Answer
C. 7.53 -
- 28.
What is x, in degrees?
- A.
42.57
- B.
34.08
- C.
0.56
- D.
55.92
- E.
0.42
Correct Answer
D. 55.92 -
- 29.
True or false? Two right triangles are similar if the acute angles of one triangle are congruent to the acute angles of the other triangle.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
Two right triangles are similar if the acute angles of one triangle are congruent to the acute angles of the other triangle. This is because in similar triangles, the corresponding angles are congruent. In right triangles, the acute angles are complementary, meaning that the sum of their measures is 90 degrees. Therefore, if the acute angles of two right triangles are congruent, it implies that the third angles are also congruent, resulting in similar triangles.Rate this question:
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- 30.
Which of the following are Pythagorean triples? Check all that apply.
- A.
7, 12, 14.1
- B.
25, 60, 72.4
- C.
25, 60, 65
- D.
5, 12, 13
- E.
8, 16, 17
- F.
16, 30, 34
Correct Answer(s)
C. 25, 60, 65
D. 5, 12, 13
F. 16, 30, 34 -
- 31.
Which of the following are not congruence theorems for right triangles? Check all that apply.
- A.
HL
- B.
HA
- C.
HH
- D.
LA
- E.
LL
- F.
AA
Correct Answer(s)
C. HH
F. AAExplanation
The two congruence theorems for right triangles are HL (hypotenuse-leg) and HA (hypotenuse-angle). HH (hypotenuse-hypotenuse) and AA (angle-angle) are not congruence theorems for right triangles.Rate this question:
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- 32.
A 45-45-90 triangle has a hypotenuse of 12√2, what is the length of one of it's legs?
Correct Answer(s)
12Explanation
In a 45-45-90 triangle, the two legs are congruent, meaning they have the same length. The hypotenuse is equal to the length of one leg multiplied by the square root of 2. In this case, the hypotenuse is given as 12√2, so the length of one leg can be found by dividing the hypotenuse by √2. Simplifying this, we get 12 as the length of one of the legs.Rate this question:
- 33.
In a 30-60-90 triangle the hypotenuse is 42, what is the length of the side opposite from the 30 degree angle?
Correct Answer(s)
21Explanation
In a 30-60-90 triangle, the side opposite the 30 degree angle is half the length of the hypotenuse. Therefore, if the hypotenuse is 42, the length of the side opposite the 30 degree angle would be half of that, which is 21.Rate this question:
- 34.
On the square baseball diamond, the distance from first base to second base is 90 feet. What is the distance from 2nd base to home plate?(Round your answer to two decimal places)
Correct Answer(s)
127.28Explanation
The distance from second base to home plate on a square baseball diamond is the same as the distance from first base to second base, which is given as 90 feet. Therefore, the distance from second base to home plate is also 90 feet. However, in the given answer, the distance is stated as 127.28 feet. This is incorrect and does not match the actual distance on a baseball diamond.Rate this question:
- 35.
A ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. This mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. When the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak? (Round your answer to two decimal places)
Correct Answer(s)
311.14Explanation
The distance, d, that a tourist will travel from the base of the mountain to its peak can be calculated using trigonometry. The vertical height of the mountain is given as 200 yards and the angle of ascent of the ski lift is given as 40 degrees. Using the sine function, we can calculate the distance traveled by multiplying the vertical height by the sine of the angle. Therefore, d = 200 * sin(40) = 311.14 yards.Rate this question:
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