1.
What is the value of a?
Solution: sin(68°)=8.5/a. Therefore a=8.5/sin(68°)≈9.2.
2.
A guy wire is attached to a tower at a point that is 7.5 m above the ground. The angle of inclination of the wire is 67°. Determine the length of the wire to the nearest tenth of a metre.
Solution: sin(67°)=7.5/x. Therefore x=7.5/sin(67°)≈8.1 m.
3.
In the following triangle, the sine of what angle is 12/13?
Solution: sine = opposite/hypotenuse. sin X = 12/13, so the angle is X.
4.
A rope that anchors a hot air balloon to the ground is 136 m long. The balloon is 72 m above the ground. What is the angle of inclination of the rope to the nearest tenth of a degree?
Solution: sin(A)=72/136=0.5294. Therefore A=sin⁻¹(0.5294)≈32.0°.
5.
A balloon is flying at the end of a 170-m length of string, which is anchored to the ground. The angle of inclination of the string is 50°. Calculate the height of the balloon to the nearest metre.
Solution: sin(50°)=x/170. Therefore x=170×sin(50°)≈130 m.
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