1.
Which equation correctly determines the length of side x?
Solution: sin(60°)=15/x. Therefore x=15/sin(60°).
2.
Determine sin G to the nearest hundredth.
Solution: sin G = opposite/hypotenuse = 84/85 ≈ 0.99.
3.
A roof rises 45 cm for every 200 cm of roof. What is the angle of elevation of the roof?
Solution: sin(x)=45/200. Therefore x=sin⁻¹(45/200)≈13°.
4.
A roof rises 1 m for every 2 m of roof. What is the angle of elevation of the roof?
Solution: sin(x)=1/2. Therefore x=sin⁻¹(1/2)=30°.
5.
A tree broke 14 ft above the ground. The top of the tree now touches the level ground and the trunk is still partially attached to the stump. The angle of inclination of the tree is 43°. To the nearest foot, determine the height of the tree before it broke.
Solution: sin(43°)=14/x, so x≈20.53 ft. Total height = 14+20.53=34.53 ft ≈ 35 ft.
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