Question

telephone wire 90feetlong is attached to the top of the building making an angle of 36 with the ground find the height of the building
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Answer 1

Given:

Telephone wire 90 feet long is attached to the top of the building making an angle of 36 with the ground

To find:

The height of the building

Solution:

The length of the telephone wire = 90 feet

The angle of elevation of the top of the building = 36°

Considering the situation in the form of right-angled triangle ABC, we have

AC = telephone wire = Hypotenuse = 90 ft

AB = height of the building = Perpendicular

∠ACB = θ = angle of elevation = 36°

By using one of the trigonometric ratios of a triangle, we get

$sin\:\theta = \frac{Perpendicular}{Hypotenuse}$

$\implies sin\: 36\° = \frac{AB}{AC}$

$\implies sin\: 36\° = \frac{AB}{90}$

$\implies 0.5877 \times 90 = AB$

$\implies \bold{AB = 52.89\:ft}$

Thus, the height of the building is → 52.89 ft.

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