Q: A ship leaves port on a bearing of $$N\ 56^ ext{o}\ W$$ for $$3.0$$ hours at a speed of $$18$$ knots (nautical miles per hour). How far is the ship from port after this time?

$$54.0\ \text{nautical miles}$$

Q: Which of the following is the correct formula for converting radians to degrees?

$$\text{degrees} = \text{radians} \times \frac{180}{\pi}$$

Q: Which of the following is the correct definition of the cotangent function?

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

Question 1

A radar station A and station B are 8 km apart on an east-west line. Station A detects a plane at a bearing of $$53^	ext{o}$$, and station B detects the same plane at a bearing of $$323^	ext{o}. $$What is the distance from station B to the plane? (Assume bearings are measured clockwise from north.)

Accepted Answer

$$7.1\ 	ext{km}$$

Question 2

Convert $$\displaystyle \frac{11\pi}{12}$$ radians to degrees. State the exact simplified answer.

Accepted Answer

$$165^	ext{o}$$

Question 3

A ship leaves port on a bearing of $$N\ 56^	ext{o}\ W$$ for $$3.0$$ hours at a speed of $$18$$ knots (nautical miles per hour). How far is the ship from port after this time?

Accepted Answer

$$54.0\ 	ext{nautical miles}$$

Question 4

A student stands $$35 ft $$from a building and measures the angle of elevation to the top as $$74.2^	ext{o}. $$She then walks back $$35 ft $$and measures the angle of elevation as $$51.8^	ext{o}. $$What is the height of the building?

Accepted Answer

$$90.1\ 	ext{ft}$$

Question 5

What is $$\cos\left(\frac{5\pi}{6}\right)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 6

Evaluate $$\cot\left(\frac{3\pi}{4}\right).$$

Accepted Answer

$$-1$$

Question 7

Find $$\sec\left(\frac{5\pi}{3}\right).$$

Accepted Answer

Question 8

A rope is wound around a drum with radius $$0.327\ 	ext{m}. If $$the drum is rotated through an angle of $$132.6^	ext{o}$$, how much rope is wound around the drum?

Accepted Answer

$$0.76\ 	ext{m}$$

Question 9

The smaller gear in a system rotates through an angle of $$150^	ext{o}$$; the larger gear has a radius of $$5.4\ 	ext{cm}$$ and the smaller gear has a radius of $$2.7\ 	ext{cm}. $$Through how many degrees will the larger gear rotate?

Accepted Answer

$$75^	ext{o}$$

Question 10

Convert $$-\frac{7\pi}{6}$$ radians to degrees.

Accepted Answer

$$-210^	ext{o}$$

Question 11

A triangle has sides $$a = 8$$, $$b = 5$$, and included angle $$C = 54^	ext{o}. $$What is the area of the triangle?

Accepted Answer

$$16.3$$

Question 12

Which of the following is the correct formula for converting radians to degrees?

Accepted Answer

$$	ext{degrees} = 	ext{radians} 	imes \frac{180}{\pi}$$

Question 13

If $$\sin	heta = 0.307$$, what is $$	heta in $$degrees?

Accepted Answer

$$17.9^	ext{o}$$

Question 14

A sector of a circle has a radius of $$5 cm $$and a central angle of $$108^	ext{o}. $$What is the length of the arc?

Accepted Answer

$$9.42\ 	ext{cm}$$

Question 15

Which of the following is the correct definition of the cotangent function?

Accepted Answer

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

Question 16

A triangle has sides $$a = 7$$, $$b = 9$$, and angle $$C = 135^	ext{o}. $$What is the area of the triangle?

Accepted Answer

$$44.6$$

Question 17

If the angle of elevation to the top of a building is $$60^	ext{o}$$ from a point $$40 ft $$away, what is the height of the building?

Accepted Answer

$$69.3\ 	ext{ft}$$

Question 18

What is the value of $$\sin(108^	ext{o})$$?

Accepted Answer

$$0.951$$

Question 19

A circular track has a radius of $$100 m. $$How far does a runner travel if she runs along an arc subtending a central angle of $$54^	ext{o}$$?

Accepted Answer

$$94.2\ 	ext{m}$$

Trigonometry Problem Set: Angles, Radian Measure, and Applications

Study Guide - Practice Questions

Study Guide - Flashcards