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The angles of elevation of the top of a rock at the top and foot of a 100 m high tower, is $30 °$ and $45 °$ . What will be the height of the rock?

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236.602m

235.602m

236.100m

236m

answer is A.

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Detailed Solution

Given that,
The height of the tower =

100

m
The angle of elevation from the top of the tower =

30 °

The angle of elevation from the foot of the tower =

45 °

We draw the schematic diagram,
Question Image

We use the trigonometric identity

tan θ = h e i g h t b a s e

.
The distance CB from the triangle

Δ A B C

tan 45 ° = A B C B ⇒ 1 = H C B [∵ tan 45 ° = 1] ⇒ C B = H

The height of the rock from triangle

Δ D A E

tan 30 ° = A E D E ⇒ tan 30 ° = H − B E H ∵ D E = C B ⇒ 13 = H − 100 H [∵ tan 30 ° = 13]

⇒ H = 3 H − 1003 ⇒ H 1 − 3 = − 1003 ⇒ H 1 − 1.732 = − 100 × 1.732 ⇒ H = = − 173.2 − 0.732 ⇒ H = 236.602 m

Thus, the height of the rock will be

236.602

m.
Therefore the correct option is 1.

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