Geometry Review: Using Trigonometry to Find an Angle

In the diagram of right triangle ABC shown below, AB = 14 and AC = 9. What is the measure of ∠A, to the nearest degree?

• 33°

• 40°

• 50°

• 57°

In the diagram of △ABC below, m∠C = 90°, CB = 13, and AB = 16. What is the measure of ∠A, to the nearest degree?

• 36°

• 39°

• 51°

• 54°

In the diagram of △RST below, m∠T = 90°, RS = 65, and ST = 60. What is the measure of ∠S, to the nearest degree?

• 23°

• 43°

• 47°

• 67°

In the diagram below of right triangle SUN, where ∠N is a right angle, SU = 13.6 and SN = 12.3. What is ∠S, to the nearest degree?

• 25°

• 42°

• 48°

• 65°

To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below. What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree?

• 4.76°

• 4.78°

• 85.22°

• 85.24°

Many roofs are slanted to prevent the buildup of snow. As modeled below, the length of a roof is 5.5 meters and it rises to a height of 2.5 meters. The angle of elevation of the roof, to the nearest degree, is

• 24°

• 25°

• 27°

• 28°

A 12-foot ladder leans against a building and reaches a window 10 feet above ground. What is the measure of the angle, to the nearest degree, that the ladder forms with the ground?

• 34

• 40

• 50

• 56

In right triangle ABC, hypotenuse AB has a length of 26 cm, and side BC has a length of 17.6 cm. What is the measure of angle B, to the nearest degree?

• 48°

• 47°

• 43°

• 34°

A man who is 5 feet 9 inches tall casts a shadow of 8 feet 6 inches. Assuming that the man is standing perpendicular to the ground, what is the angle of elevation from the end of the shadow to the top of the man’s head, to the nearest tenth of a degree?

• 34.1

• 34.5

• 42.6

• 55.9

In the diagram below of ΔHAR and ΔNTY, angles H and N are right angles, and ΔHAR ~ ΔNTY. If AR = 13 and HR = 12, what is the measure of angle Y, to the nearest degree?

• 23°

• 25°

• 65°

• 67°