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The angle of elevation of the top of a building from the foot of the tower is $30 °$ and the angle of elevation of the top of the tower from the foot of the building is $45 °$ . If the tower is 30 m high, find the height of the building.

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203 m

303 m

403 m

503 m

answer is B.

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Detailed Solution

Given that the angle of elevation of the top of a building from the foot of the tower is

30 °

and

45 °

the angle of elevation of the top of the tower from the foot of the building is:
We have to find, if the tower is high, the height of the building.

In a right-angle triangle, tan θ = Opposite side Hypotenuse

Δ A B C

tan θ = Opposite Adjacent ⇒ tan45 ° = AB BC ⇒ tan45 ° = 30 BC ⇒ 1 = 30 BC ∴ BC = 30 m

We shall use the same in

Δ DBC

and find the value of DC and the length of D C will be equal to the height of the building
In

Δ D B C

tanθ= Opposite Adjacent ⇒ tan30 ° = DC BC ⇒ 13 = DC 30 ⇒ 30×1=DC× 3 ⇒ DC= 303 m

Therefore the height of the building is

303 m

.
Therefore, the correct option is 2.

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