Q: Which reciprocal identity is correct for $$\tan \theta$$?

$$\tan \theta = \frac{1}{\cot \theta}$$

Q: Which of the following is the correct expression for $$\cot \theta in $$terms of sides of a right triangle?

$$\frac{\text{adjacent}}{\text{opposite}}$$

Q: Which of the following is the correct reciprocal identity for $$\sec \theta$$?

$$\sec \theta = \frac{1}{\cos \theta}$$

Question 1

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 13 ft long and the base is 5 ft from the wall, what is the sine of the angle between the ladder and the ground?

Accepted Answer

$$\frac{12}{13}$$

Question 2

Which trigonometric function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle?

Accepted Answer

$$\cos 	heta$$

Question 3

Given a right triangle with sides 8, 15, and 17, what is $$\cos 	heta if$$ $$	heta is $$the angle opposite the side of length 8?

Accepted Answer

$$\frac{15}{17}$$

Question 4

A ramp rises 12 ft vertically and is 16 ft long. What is $$\sin 	heta$$ where $$	heta is $$the angle the ramp makes with the ground?

Accepted Answer

$$\frac{12}{20}$$

Question 5

Which reciprocal identity is correct for $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{1}{\cot 	heta}$$

Question 6

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in a $$right triangle, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 7

A surveyor measures the angle of elevation to the top of a building as $$35^\circ$$ from a point 50 meters away. Which trigonometric function should be used to find the height of the building?

Accepted Answer

$$	an$$

Question 8

Given $$	an 	heta = \frac{12}{5} in a $$right triangle, what is $$\sec 	heta$$?

Accepted Answer

$$\frac{13}{5}$$

Question 9

Which of the following is the correct expression for $$\cot 	heta in $$terms of sides of a right triangle?

Accepted Answer

$$\frac{	ext{adjacent}}{	ext{opposite}}$$

Question 10

If $$\cos 	heta = \frac{5}{13}$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 11

A right triangle has legs of 9 and 12 units. What is the length of the hypotenuse?

Accepted Answer

$$15$$

Question 12

Which trigonometric function is used to find the angle when the lengths of the opposite and adjacent sides are known?

Accepted Answer

$$	an$$^{-1}$$

Question 13

If $$\sin 	heta = 0.5$$, what is $$	heta in $$degrees?

Accepted Answer

$$30^\circ$$

Question 14

A construction worker needs to find the angle of a roof that rises 8 ft over a horizontal distance of 15 ft. Which equation should be used?

Accepted Answer

$$	an 	heta = \frac{8}{15}$$

Question 15

Which of the following is the correct reciprocal identity for $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 16

If $$\sin 	heta = \frac{5}{13}$$, what is $$\csc 	heta$$?

Accepted Answer

$$\frac{13}{5}$$

Question 17

A right triangle has a hypotenuse of 20 and one leg of 12. What is the length of the other leg?

Accepted Answer

$$16$$

Question 18

Which trigonometric function would you use to find the angle of elevation if you know the height and the length of the ramp?

Accepted Answer

$$	an$$

Question 19

If $$	an 	heta = \frac{3}{4}$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{3}{5}$$

Question 20

A triangle has sides of 5, 12, and 13. What is $$\cos 	heta if$$ $$	heta is $$the angle opposite the side of length 5?

Accepted Answer

$$\frac{12}{13}$$

Right Triangle Trigonometry: Functions, Identities, and Applications

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