Q: A building casts a $$15 m $$shadow when the angle of elevation of the sun is $$30^\circ. $$How tall is the building?

$$15 \tan 30^\circ = 15 \cdot \frac{1}{\sqrt{3}} = 5\sqrt{3} m$$

Question 1

Without using a calculator, give the exact value of $$\sin 45^\circ.$$

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 2

Find the exact value of $$\cos 60^\circ.$$

Accepted Answer

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

Question 3

Convert $$\frac{\pi}{3}$$ radians to degrees.

Accepted Answer

$$60^\circ$$

Question 4

Convert $$120^\circ to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 5

Suppose $$	heta is in $$standard position and the given point is on the terminal side of $$	heta. If $$the point is $$(-3, 4)$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 6

Use the Pythagorean identity to find $$\sin 	heta if$$ $$\cos 	heta = \frac{3}{5}$$ and $$	heta is in $$quadrant IV.

Accepted Answer

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

Question 7

Evaluate $$	an$$^{-1}$$(1)$$ and write your answer in radians.

Accepted Answer

$$\frac{\pi}{4}$$

Question 8

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is $$10 ft $$long, how high up the wall does it reach?

Accepted Answer

$$10 \sin 60^\circ = 5\sqrt{3} ft$$

Question 9

Find the value of $$\sin(2	heta) if$$ $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$quadrant II.

Accepted Answer

$$\frac{24}{25}$$

Question 10

A ship leaves port and sails $$8 km $$east, then $$6 km $$north. How far is the ship from the port?

Accepted Answer

$$10 km$$

Question 11

Given $$	riangle ABC$$ with $$AB = 7$$, $$BC = 24$$, and $$CA = 25$$, what is $$\sin A$$?

Accepted Answer

$$\frac{24}{25}$$

Question 12

Find the amplitude and period of $$y = 3 \sin(2x).$$

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 13

If $$	an 	heta = 2$$ and $$	heta is in $$quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 14

A Ferris wheel with a radius of $$20 m $$makes one revolution every $$40$$ seconds. What is the angular speed in radians per second?

Accepted Answer

$$\frac{\pi}{20}$$

Question 15

Find the exact value of $$\cos(\pi - x) in $$terms of $$\cos x.$$

Accepted Answer

$$-\cos x$$

Question 16

A ramp rises $$3 ft $$over a horizontal distance of $$12 ft. $$What is the angle of elevation to the nearest degree?

Accepted Answer

$$14^\circ$$

Question 17

If $$\sin \alpha = \frac{5}{13}$$ and $$\alpha is in $$quadrant II, what is $$\cos \alpha$$?

Accepted Answer

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

Question 18

A building casts a $$15 m $$shadow when the angle of elevation of the sun is $$30^\circ. $$How tall is the building?

Accepted Answer

$$15 	an 30^\circ = 15 \cdot \frac{1}{\sqrt{3}} = 5\sqrt{3} m$$

Question 19

Find the reference angle for $$210^\circ.$$

Accepted Answer

$$30^\circ$$

Question 20

A pilot flies $$100 km at a $$bearing of $$30^\circ$$, then $$100 km at a $$bearing of $$120^\circ. $$What is the straight-line distance from the starting point to the ending point?

Accepted Answer

$$173.2 km$$

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