1.
Calculate the measure of ∠GHJ to the nearest tenth of a degree.
Solution: Find GK≈6.7 cm, then GJ≈10.7 cm. tan(GHJ)=10.7/6, so GHJ≈60.7°.
2.
A surveyor takes measurements of a cliff across a river. What is the height of the cliff?
Solution: Find x≈38 m, then h≈71.5 m≈72 m.
3.
In the diagram at the right find the value of x. (Accurate to the nearest tenth.)
Solution: sin(30°)=y/10 so y=5. Then cos(45°)=x/5, so x≈3.5.
4.
Two buildings are 30 m apart. From the roof of the shorter building, the angle of elevation of the top of the other building is 25° and the angle of depression of the base is 30°. Find the height of the taller building.
Solution: 30tan(30°)+30tan(25°)≈31.3 m.
5.
A road rises 1 m for every 19 m measured along the road. To the nearest tenth of a metre, how far does a car travel horizontally when it travels 300 m along the road?
Solution: Angle≈3°. Horizontal distance=300×cos(3°)≈299.6 m.
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