1.
Which equation can be used to correctly determine the length of side r?
Solution: Tangent = opposite/adjacent. Therefore tan(25°)=r/12.
2.
The angle between one shorter side of a rectangle and a diagonal is 64°. One longer side of the rectangle is 9.2 cm. What is the width of the rectangle, to the nearest tenth of a centimetre?
Solution: tan(64°)=9.2/x. Therefore x≈4.49 cm ≈ 4.5 cm.
3.
Determine tan Q and tan R.
Solution: tan Q = 16/12 = 4/3 = 1.33 and tan R = 12/16 = 3/4 = 0.75.
4.
An airplane is flying at an altitude of 7000 m. At a certain time, the angle between the ground and a person's line of sight to the airplane is 22°. About how far away is the person from a point on the ground vertically below the airplane, to the nearest hundred metres?
Solution: tan(22°)=7000/x. Therefore x=7000/tan(22°)≈17325.6 m ≈ 17 300 m.
5.
Find x.
Solution: tan(15°)=x/25. Therefore x=25×tan(15°)≈6.7.
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