1.
What is the measure of angle D?
Solution: tan(D)=3/2, so D≈56°.
2.
Determine the measure of ∠B to the nearest tenth.
Solution: sin(B)=17/25, so B≈42.8°.
3.
A balloon is flying at the end of a 170‑m string. Angle of inclination 50°. Calculate the height.
Solution: h=170sin(50°)≈130 m.
4.
A tree broke 14 ft above the ground. Angle of inclination 43°. Determine original height.
Solution: Broken part≈20.5 ft; total≈35 ft.
5.
Given the following triangle, what is the length of side MP to one decimal place?
Solution: sin(25°)=7/MP, so MP≈16.6.
6.
A rectangle width 5.1 cm and diagonal 9.3 cm. Find the angle between diagonal and shorter side.
Solution: cos=5.1/9.3, angle≈56.7°.
7.
In triangle PQR, what is cos P?
Solution: Cosine = adjacent/hypotenuse = QP/PR.
8.
A helicopter is 200 m above a road. A car is 300 m away (line of sight). What is the angle of elevation?
Solution: sin(θ)=200/300, so θ≈42°.
9.
Find the measure of angle BAC to the nearest degree.
Solution: tan(BAC)=7/10, so BAC≈35°.
10.
A ladder is 8.0 m long and has angle of inclination 72°. How far from the wall is the base?
Solution: x=8cos72°≈2.5 m.
11.
Two trees are 96 yd apart. From halfway between them, angles of elevation are 10° and 19°. How much taller is one tree?
Solution: Heights differ by about 8.1 yd.
12.
Determine the perimeter of this rhombus to the nearest tenth.
Solution: Side≈4.12 cm, perimeter≈16.5 cm.
13.
Determine the measure of ∠V to the nearest tenth of a degree.
Solution: cos(V)=8.9/15.1, so V≈53.9°.
14.
Find x.
Solution: tan(15°)=x/25, so x≈6.7.
15.
Two trees are 55 yd apart. From halfway between them, determine the height of each tree.
Solution: Heights≈19 yd and 15 yd.
16.
Determine the length of AC to the nearest tenth of a centimeter.
Solution: AC≈24.84+17.05=41.9 cm.
17.
A guy wire is attached 5.5 m above the ground. The angle with the ground is 56°. How far from the base is it anchored?
Solution: tan(56°)=5.5/x, so x≈3.7 m.
18.
From the top of a lighthouse, 40.0 m above the sea, the angle of depression to a boat is 20°. How far is the boat from the base?
Solution: tan(20°)=40/x, so x≈109.9 m.
19.
Solve this right triangle. Give measures to the nearest tenth.
Solution: ∠G=40°, GH≈21.8 cm, FH≈18.3 cm.
20.
A ladder is 5 m long. The base is 1.0 m from the wall. What angle does it make with the ground?
Solution: cos=1/5, angle≈78.5°.
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