Question 1

Which of the following is an expression that generates all angles coterminal with $$45^\circ$$? Let $$n be $$any integer.

Accepted Answer

$$45^\circ + 360n$$

Question 2

Given the triangle in Figure 17 with angles $$48^\circ$$, $$61^\circ$$, and $$x$$, what is the value of $$x$$?

Accepted Answer

Question 3

Given $$	an 	heta = -\frac{15}{8}$$ and $$	heta is in $$quadrant II, what is $$\sin 	heta$$?

Accepted Answer

Question 4

A building 10 m high casts a shadow 18 m long. At the same time, a flagpole casts a shadow 27 m long. What is the height of the flagpole?

Accepted Answer

$$15 m$$

Question 5

Find all values of $$	heta in$$ $$[0^\circ, 360^\circ)$$ such that $$\cos 	heta = -\frac{\sqrt{2}}{2}.$$

Accepted Answer

$$135^\circ, 225^\circ$$

Question 6

Given a right triangle with legs $$a = 5$$, $$b = 12$$, find the hypotenuse $$c.$$

Accepted Answer

$$c = 13$$

Question 7

Find the coordinates of the point on a circle of radius $$6$$ centered at the origin that corresponds to an angle of $$150^\circ in $$standard position.

Accepted Answer

$$(-3, 3\sqrt{3})$$

Question 8

Given $$\sin 	heta = \frac{2}{3}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{\sqrt{5}}{3}$$

Question 9

A house is $$15 ft $$tall and casts a shadow $$40 ft $$long. At the same time, a nearby building casts a shadow $$300 ft $$long. What is the height of the building?

Accepted Answer

$$112.5 ft$$

Question 10

Solve for $$x in $$Figure 15 if $$\angle 1 = (3x + 2)^\circ$$ and $$\angle 4 = (5x - 40)^\circ$$ and $$m \parallel n.$$

Accepted Answer

$$x = 14$$

Question 11

Given a right triangle with $$c = 12.7 in $$and $$A = 34^\circ 30'$$, find the length of side $$a ($$opposite $$A).$$

Accepted Answer

Question 12

Find the angle of elevation of the sun if a building $$34.09 m $$tall casts a shadow $$37.62 m $$long. Round to the nearest hundredth of a degree.

Accepted Answer

$$42.99^\circ$$

Question 13

Which of the following is a coterminal angle with $$270^\circ$$?

Accepted Answer

$$-90^\circ$$

Question 14

Given $$\sin 	heta = 0.9271$$, find two angles in $$[0^\circ, 360^\circ)$$ that satisfy this equation (rounded to the nearest degree).

Accepted Answer

$$68^\circ, 112^\circ$$

Question 15

A triangle has sides of $$4 cm$$, $$5 cm$$, and $$7 cm. If $$the shortest side of the actual piece of land is $$400 m$$, what are the lengths of the other two sides?

Accepted Answer

$$500 m$$, $$875 m$$

Question 16

Given $$	an 	heta = 0.7002$$, find two angles in $$[0^\circ, 360^\circ)$$ that satisfy this equation (rounded to the nearest degree).

Accepted Answer

$$35^\circ, 215^\circ$$

Question 17

If $$\sin 	heta = \frac{\sqrt{3}}{2}$$, what are all possible values of $$	heta in$$ $$[0^\circ, 360^\circ)$$?

Accepted Answer

$$60^\circ, 120^\circ$$

Question 18

A right triangle has legs $$a = 3$$, $$b = 4. $$What is the value of $$\sin B$$ where $$B is $$the angle opposite side $$b$$?

Accepted Answer

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

Question 19

A flagpole casts a shadow $$27 m $$long at the same time a $$10 m $$building casts a shadow $$18 m $$long. What is the height of the flagpole?

Accepted Answer

$$15 m$$

Coterminal Angles and Expressions for All Coterminal Angles

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