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The angle of elevation of the top of a building from the foot

Question

The angle of elevation of the top of a building from the foot of the tower is 30 $^{o}$ and the angle of elevation of the top of the tower from the foot of the building is 60 $^{o}$ . If the tower is 48 meters high, find the height of the building (in m.)

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Sebastian Discussed

The angle of elevation of the top of a building from the foot of the tower is 30

^{o}

and the angle of elevation of the top of the tower from the foot of the building is 60

^{o}

. If the tower is 48 meters high, find the height of the building (in m.)

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Text solutionVerified

The situation in the problem is shown in the attached figure.

Given:

CE = 48 m

∠ EBC = 6 0^{o}

∠ A CB = 3 0^{o}

To find:

A B

Using trigonometric identity,

tan (∠ EBC) = \frac{EC}{BC} ........... (i)

tan (∠ A CB) = \frac{A B}{BC} ........... (ii)

Dividing (ii) by (i),

\frac{A B}{EC} = \frac{tan ( ∠ A CB )}{tan ( ∠ EBC )}

Substituting values,

\frac{A B}{48} = \frac{tan 3 0 ^{o}}{tan 6 0 ^{o}}

\frac{A B}{48} = \frac{1/ 3}{3}

A B = \frac{48}{3} = 16 m

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Question Text	The angle of elevation of the top of a building from the foot of the tower is 30 $^{o}$ and the angle of elevation of the top of the tower from the foot of the building is 60 $^{o}$ . If the tower is 48 meters high, find the height of the building (in m.)
Answer Type	Text solution:1
Upvotes	151