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Question

The upper part of a tree broken over by the wind makes an angle of 30 with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree.

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Solution

BC=15 m, AB=hFrom the diagram we can calculate,A=60Using sine rule,sin A15=sin Ch sin 6015=sin 30h 32×15=12×h 315=1h h=153 h=53

h=53Also,15sin 60=ysin 90 1532=y y=303=103So,the height of the true is h+y=53+10 3 m=153 m


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