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From two points A and B on the same side of a building the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distances between A and B correct to two decimal places

(a) 10.66 m

(b) 13.43 m

(c) 11.55 m

(d) 12.26 m

1 Answer

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Best answer

Correct option is (c) 11.55 m

Let CD is building A and B are two given points using horizontally on the same side of building.

In ΔDBC,

tan 60° = \(\frac{DC}{CB}\)

\(\sqrt 3 = \frac{10}y\)    ......(1)

In ΔDCA,

tan 30° = \(\frac{DC}{CA}\)

\(\frac 1{\sqrt 3} = \frac{10}{x + y}\)    .......(2)

From (1), put y = \(\frac{10}{\sqrt 3}\) in (2), we get

\(\frac 1{\sqrt 3} = \frac{10}{x + \frac{10}{\sqrt 3}}\)

\(\frac 1{\sqrt 3} = \frac{10\sqrt 3}{\sqrt 3x + 10}\)

\(30 = \sqrt 3x + 10\)

\(x = \frac{20}{\sqrt 3}\)

\(x = 11.55\) m

Hence, distance between two points A and B is 11.55 m.

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