Right Triangle Trig Quiz 4.6.3

1. For the right triangle ABC shown below, what is tanA?

A/c

B/c

A/b

B/a

C/b

In a right triangle, the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, angle A is opposite side a and adjacent to side b. Therefore, the tangent of angle A is a/b.

Explanation

In a right triangle, the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, angle A is opposite side a and adjacent to side b. Therefore, the tangent of angle A is a/b.

2. The hypotenuse of the right triangle LMN shown below is 22 feet long. The cosine of angle L is ¾. How many feet long is the segment LM?

18.4

16.5

11.0

6.7

4.7

The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In this case, the cosine of angle L is ¾. Therefore, the length of the adjacent side (LM) is ¾ of the length of the hypotenuse. Since the hypotenuse is 22 feet long, the length of LM is ¾ * 22 = 16.5 feet.

Explanation

The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In this case, the cosine of angle L is ¾. Therefore, the length of the adjacent side (LM) is ¾ of the length of the hypotenuse. Since the hypotenuse is 22 feet long, the length of LM is ¾ * 22 = 16.5 feet.

3. For the right triangle ABC shown below, what is SinA?

B/c

A/c

A/b

B/a

C/a

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this triangle, side a is opposite angle A and side c is the hypotenuse. Therefore, the sine of angle A is a/c.

Explanation

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this triangle, side a is opposite angle A and side c is the hypotenuse. Therefore, the sine of angle A is a/c.

4.

Note: fractions are written using the slash. You will need to draw the triangle.

A

B

C

D

E

not-available-via-ai

Explanation

not-available-via-ai

5. The hypotenuse of the right triangle ABC shown below is 17 feet long. The cosine of angle C is 3/5. How many feel long is segment AC?

A. 6 B. 10.2 C. 12 D. 15 E. 28.3

6

10.2

12

15

28.3

The cosine of angle C is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is segment AC and the hypotenuse is 17 feet. So, we can set up the equation cos(C) = AC/17. Given that cos(C) = 3/5, we can substitute this value into the equation to solve for AC. Cross multiplying, we get 5(AC) = 3(17), which simplifies to AC = 51/5 = 10.2 feet. Therefore, segment AC is 10.2 feet long.

Explanation

The cosine of angle C is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is segment AC and the hypotenuse is 17 feet. So, we can set up the equation cos(C) = AC/17. Given that cos(C) = 3/5, we can substitute this value into the equation to solve for AC. Cross multiplying, we get 5(AC) = 3(17), which simplifies to AC = 51/5 = 10.2 feet. Therefore, segment AC is 10.2 feet long.

6. When measured from a point on the ground that is a certain distance from the base of a cell phone tower, the angle of elevation to the top of the tower is 41°, as shown below. The height of the cell phone tower is 200 feet. What is the distance, in feet to the cell
phone tower?

230.1 feet

131.2 feet

150.9 feet

265.0 feet

173.9 feet

The angle of elevation to the top of the tower is given as 41°. Using trigonometry, we can use the tangent function to find the distance to the tower. 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 tower (200 feet) and the adjacent side is the distance to the tower. So, we have tan(41°) = 200/distance. Solving for distance, we get distance = 200/tan(41°) ≈ 230.1 feet. Therefore, the distance to the cell phone tower is approximately 230.1 feet.

Explanation

The angle of elevation to the top of the tower is given as 41°. Using trigonometry, we can use the tangent function to find the distance to the tower. 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 tower (200 feet) and the adjacent side is the distance to the tower. So, we have tan(41°) = 200/distance. Solving for distance, we get distance = 200/tan(41°) ≈ 230.1 feet. Therefore, the distance to the cell phone tower is approximately 230.1 feet.

7. A ladder leans against a house at an angle of elevation of 50 degrees. How long is the ladder if the bottom of the ladder is 10 feet from the base of the house? Round to the nearest tenth of a foot.

15.6 feet

6.4 feet

13.1 feet

11.9 feet

8.4 feet

The ladder forms a right triangle with the ground and the side of the house. The angle of elevation is given as 50 degrees. The length of the ladder is the hypotenuse of the triangle. The base of the triangle is given as 10 feet. To find the length of the ladder, we can use the trigonometric function tangent. tan(50 degrees) = opposite/adjacent. The opposite side is the length of the ladder and the adjacent side is 10 feet. Rearranging the formula, we get length of the ladder = 10 feet / tan(50 degrees) = 15.6 feet.

Explanation

The ladder forms a right triangle with the ground and the side of the house. The angle of elevation is given as 50 degrees. The length of the ladder is the hypotenuse of the triangle. The base of the triangle is given as 10 feet. To find the length of the ladder, we can use the trigonometric function tangent. tan(50 degrees) = opposite/adjacent. The opposite side is the length of the ladder and the adjacent side is 10 feet. Rearranging the formula, we get length of the ladder = 10 feet / tan(50 degrees) = 15.6 feet.

8. The perimeter of a square is 36 units. How many units long is the diagonal of the square?
You need to draw the square.

A

B

C

D

E

To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, all sides are equal in length. Let's assume that the length of one side of the square is 's'. The perimeter of the square is given as 36 units, so 4s = 36. Dividing both sides by 4, we get s = 9. Now, we can use the Pythagorean theorem to find the length of the diagonal. The diagonal of a square divides it into two congruent right triangles. Using the theorem, we have d^2 = s^2 + s^2 = 2s^2. Substituting the value of 's' as 9, we get d^2 = 2(9^2) = 162. Taking the square root of both sides, we get d = √162. Therefore, the length of the diagonal is √162 units.

Explanation

To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, all sides are equal in length. Let's assume that the length of one side of the square is 's'. The perimeter of the square is given as 36 units, so 4s = 36. Dividing both sides by 4, we get s = 9. Now, we can use the Pythagorean theorem to find the length of the diagonal. The diagonal of a square divides it into two congruent right triangles. Using the theorem, we have d^2 = s^2 + s^2 = 2s^2. Substituting the value of 's' as 9, we get d^2 = 2(9^2) = 162. Taking the square root of both sides, we get d = √162. Therefore, the length of the diagonal is √162 units.

9. What is the sin(60)

Note, the fractions are written as slashes.

A

B

C

D

E

The correct answer is A because sin(60) is equal to 1/2. In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. In a 30-60-90 triangle, the side opposite the 60-degree angle is equal to half the length of the hypotenuse. Therefore, sin(60) is equal to 1/2.

Explanation

The correct answer is A because sin(60) is equal to 1/2. In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. In a 30-60-90 triangle, the side opposite the 60-degree angle is equal to half the length of the hypotenuse. Therefore, sin(60) is equal to 1/2.