Question

The angle of depression of a point 100 mts . from the foot of the tree is 60° . How tall is the tree ? ​

Answer 1

Answer:

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➡️ let

AB = h meters

➡️ Given angle XAC = 60°

:. angle BCA = 60°

➡️ ( :. angle XAC = angle BCA ( Alternate angles ) )

BC = 100 meters

From ∆ ACB

tan 60° = $\frac{AB}{BC}$

√3 = $\frac{h}{100}$

:. h = 100 √3

=> 100 × 1.732

=> 173.2 meters

:. Height of the tree = $\bf\green{173.2~meters}$

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