Trigonometry With Right Triangles Assessment Test

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1/10 Questions

What is equal to the root of the square of the opposite?
- Adjacent
- Pythagoras
- Hypotenuse
- All of the above

About This Quiz

Take this assessment test to evaluate your knowledge of trigonometry with right triangles. What are sine, cosine, and tangent? How can we use them to solve for unknown sides and angles in right triangles?

Trigonometry With Right Triangles Assessment Test - Quiz

2.

The side opposite the right angle is called...
- Opposite
- Hypotenuse
- Adjacent
- None of the above
Correct Answer

A. Hypotenuse

Explanation

The side opposite the right angle in a right triangle is called the hypotenuse. The hypotenuse is the longest side of the triangle and is always opposite the right angle. It is found by 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 hypotenuse is the correct answer because it accurately describes the side opposite the right angle.

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3.

The division of the opposite side of a right angle with the adjacent side gives...
- Sin
- Tan
- Cot
- Cos
Correct Answer

A. Tan

Explanation

The division of the opposite side of a right angle with the adjacent side gives the tangent (Tan) of the angle.

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4.

Given that a right angle has opposite sides a and b equals 4cm and 3cm, calculate the length of the hypotenuse.
- 4cm
- 5cm
- 6cm
- 7cm
Correct Answer

A. 5cm

Explanation

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. According to the Pythagorean theorem, 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 square of the hypotenuse is equal to 4^2 + 3^2, which is 16 + 9 = 25. Taking the square root of 25 gives us the length of the hypotenuse, which is 5cm.

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5.

Pythagoras theorem states that...
- √a+√b=c2
- A2+b2=c
- √a2+b2=√c2
- √a2-b2=√c2
Correct Answer

A. √a2+b2=√c2

Explanation

The given answer, √a2+b2=√c2, is the correct statement of the Pythagoras theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Thus, taking the square root of both sides of the equation gives us √a2+b2=√c2, which represents the Pythagoras theorem accurately.

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6.

Sin 30° = ?
- 1/2
- 1/3
- 1/4
- 1/5
Correct Answer

A. 1/2

Explanation

The correct answer is 1/2. The sine of 30 degrees is equal to 1/2. In trigonometry, the sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, sin 30 degrees equals 1/2.

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7.

If sin a=-1/2, solve for 0°.
- 30° and 150°
- 150° and 210°
- 210° and 330°
- 150° and 330°
Correct Answer

A. 210° and 330°

Explanation

The sine function is negative in the third and fourth quadrants. Since sin a = -1/2, we know that the reference angle is 30°. In the third quadrant, the angle is 180° + 30° = 210°. In the fourth quadrant, the angle is 360° - 30° = 330°. Therefore, the solutions are 210° and 330°.

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8.

If tan b=5/4 find sin2b-cos2b.
- - 41/9
- 5/4
- 1
- 9/41
Correct Answer

A. 9/41

Explanation

To find sin2b-cos2b, we need to use the trigonometric identities. We know that sin2b = 2sinb*cosb and cos2b = cos^2b - sin^2b. From the given information, we have tan b = 5/4. We can use this to find sinb and cosb. We know that tan b = sinb/cosb, so sinb = 5 and cosb = 4. Now we can substitute these values into the identities. sin2b = 2(5)(4) = 40 and cos2b = (4)^2 - (5)^2 = 16 - 25 = -9. Therefore, sin2b-cos2b = 40 - (-9) = 40 + 9 = 49. However, none of the answer choices match 49, so the correct answer is not given.

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9.

A man 40m from the foot of a tower observes the angle of elevation of the tower to be 30°. Determine the height of the tower.
- 40√3/3
- 40
- 40√3
- 20
Correct Answer

A. 40√3/3

Explanation

The man is standing 40m away from the foot of the tower. He observes the angle of elevation of the tower to be 30°. To determine the height of the tower, we can use the tangent of the angle of elevation. The tangent of 30° is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the man to the foot of the tower). Therefore, the height of the tower is 40√3/3.

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10.

If sin c = 3/5, find tan c.
- 3/5
- 3/4
- 2/3
- 1/4
Correct Answer

A. 3/4

Explanation

If sin c = 3/5, we can use the Pythagorean identity sin^2 c + cos^2 c = 1 to find cos c. Since sin c = 3/5, we can square it to get (3/5)^2 = 9/25. Subtracting this from 1 gives us 1 - 9/25 = 16/25. Taking the square root of this gives us cos c = 4/5. To find tan c, we can divide sin c by cos c, giving us (3/5)/(4/5) = 3/4. Therefore, the correct answer is 3/4.

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