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Find the height of a tree of angle of elevation of its top changes from 25 degree to 50 degree as the observer advance 15m towards its base

please help me fast​

1 Answer

8 votes

Answer:

11.5 m

Explanation:

The problem can be solved using a trig relation that relates the side opposite the angle to the side adjacent to the angle. That relation is ...

Tan = Opposite/Adjacent

The lengths of the adjacent sides of the triangle can be found by rearranging this formula:

Adjacent = Opposite/Tan

__

The "opposite" side of the triangle is the height of the tree, which we can represent using h. The problem statement tells us of a relation between adjacent side lengths and angles:

h/tan(25°) -h/tan(50°) = 15 . . . . . moving 15 meters changes the angle

h(1/tan(25°) -1/tan(50°)) = 15

h = 15·tan(25°)·tan(50°)/(tan(50°) -tan(25°)) = 15(0.55572/0.72545)

h ≈ 11.4907 . . . . meters

The height of the tree is about 11.5 meters.

Find the height of a tree of angle of elevation of its top changes from 25 degree-example-1
User Kartos
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