There is a 10 meter tower between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45°. How far are the roads from each other?

Question

Question

This question was previously asked in

Bihar STET TGT (Social Science) Official Paper-I (Held On: 06 Sept, 2023 Shift 1)

Answer 1

Given:

The angle of depression of P = 45∘

The angle of depression of Q = 30∘

Height = 10 m

Concept:

The angle of depression: The angle formed by the line of sight and the horizontal plane for an object below the horizontal.

tanθ = perpendicular/base = P/B

tan45∘ = 1 and tan30∘ = 1/√3

Calculation:

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PS = 10 m

tan45∘ = 1 = PS/RS

∴ PS = RS = 10 m

tan30∘ = 1/√3 = PS\RQ

RQ = 10√3

RQ = RS + SQ

RQ = 10 + 10√3

= 10 + 17.32

= 27.32 m

The distance between roads is 27.32 m