Question 1

A pendulum swings through an angle of $$40^\circ$$ each second. If the pendulum is 45 inches long, how far does its tip move each second? (Round your answer to two decimal places.)

Accepted Answer

$$31.42 in.$$

Question 2

The blade of a windshield wiper sweeps out an angle of $$135^\circ in $$one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle? (Round to the nearest $$0.1$$ square inch.)

Accepted Answer

$$1041.8\ 	ext{in}^2$$

Question 3

From the edge of a $$1000-$$foot cliff, the angles of depression to two cars in the valley below are $$21^\circ$$ and $$28^\circ. $$How far apart are the cars? (Round your answer to the nearest $$0.1 ft.)$$

Accepted Answer

$$724.5 ft$$

Question 4

A twenty-five foot ladder just reaches the top of a house and forms an angle of $$41.5^\circ$$ with the wall of the house. How tall is the house? (Round your answer to the nearest $$0.1$$ foot.)

Accepted Answer

$$18.7 ft$$

Question 5

A ladder leans against a building that has a wall slanting away from the ladder at an angle of $$96^\circ$$ with the ground. If the bottom of the ladder is $$23$$ feet from the base of the wall and it reaches a point $$52$$ feet up the wall, how tall is the ladder to the nearest foot?

Accepted Answer

$$61 ft$$

Question 6

An airplane is sighted at the same time by two ground observers who are $$3$$ miles apart and both directly west of the airplane. They report the angles of elevation as $$14^\circ$$ and $$20^\circ. $$How high is the airplane?

Accepted Answer

$$2.37$$\ mi

Question 7

To find the distance $$AB$$ across a river, a distance $$BC of$$ $$447 m is $$laid off on one side of the river. It is found that $$B = 101.1^\circ$$ and $$C = 18.1^\circ. $$Find $$AB. ($$Round to the nearest meter.)

Accepted Answer

$$159$$\ m

Question 8

Two points $$A$$ and $$B$$ are on opposite sides of a building. A surveyor selects a third point $$C to $$place a transit. Point $$C is$$ $$55$$ feet from point $$A$$ and $$72$$ feet from point $$B. $$The angle $$ACB is$$ $$53^\circ. $$How far apart are points $$A$$ and $$B$$?

Accepted Answer

$$102.9$$\ ft

Question 9

Given $$B = 84^\circ$$, $$b = 5$$, $$a = 24. $$Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.

Accepted Answer

one triangle: $$A = 41^\circ$$, $$C = 54^\circ$$, $$c = 31$$

Question 10

Given $$a = 7$$, $$b = 9$$, $$B = 49^\circ. $$Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.

Accepted Answer

two triangles: $$A_1 = 76.01$$^\circ$$, C_1$ = 54.99^\circ$$, $$c_1 = 7.60$ or A_2$ = 103.99^\circ$$, $$C_2 = 27.01$$^\circ$$, c_2$ = 12.14$$

Question 11

Find an equation for the graph shown (amplitude $$5$$, period $$6\pi$$, negative sine function).

Accepted Answer

$$y = -5 \sin \left( \frac{1}{3}x \right)$$

Precalculus Study Guidance: Trigonometry, Geometry, and Graphs

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