Question

Need help with this trigonometry word problem

From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30 degree. Find the distance between the tree and the tower.
Please show your work

Answer 1

30√3 m ≈ 52 m

Explanation:

The side ratios in a 30°-60°-90° triangle are 1 : √3 : 2. The long leg of the triangle is √3 times 30 m, or about 51.96 m.

The distance between the tree and the tower is about 30√3 m ≈ 52 m.

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If you haven't memorized the ratios of this special triangle, you can use the relation ...

Tan = Opposite/Adjacent

tan(30°) = 30/d

d = 30/tan(30°) = 30√3 = 51.96 . . . . same as above