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Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30 with it. The distance between the foot of the tree to the point where the top touches the ground is 9 m. Find the height of the tree.

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Solution

Let AB be the original height of the tree. Suppose it got bent at a point C and let the part CB take the position CD, meeting the ground at D. Then,



AD = 9 m , ADC=30 and CD = CB

Let AC = x metres and CD = CB = y metres

From right ΔDAC, we have

ACAD=tan 30=13x9=13

x=93x=93×33=33

Also, from right ΔDAC, we have

CDAD=sec 30=23y9=23

y=183y=183×33=63

AC=33 m and CB=63 m

Total height of the tree =33 m+63 m=93 metres

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