From the top of a house A in a street the angles of elevation and depression of the top and foot of ...........

Quantitative Aptitude (CPO) Height and Distance

From the top of a house A in a street, the angles of elevation and depression of the top and foot of another house B on the opposite

side of the street are 60^o and 45^o respectively. If the height of house A is 36 m, then what is the height of house

B? (Your answer should be nearest to an Integer.)

This questions was previously asked in

SSC CPO 9th Dec 2019 Shift-2

91 m

93 m

94 m

98 m

Let’s break this down:

From the top of House A (36 m high), you look at House B across the street.

The angle up (elevation) to B’s top: 60°. The angle down (depression) to B’s base: 45°.

Imagine a horizontal line from A’s top—call street width “x” and height of B “h”.

From A’s top to B’s foot: 45° depression, so drop of 36 m over distance x ? x = 36 m (tan 45° = 1).

From A’s top to B’s top: 60° elevation, rise of (h - 36) over same distance x ? tan 60° = (h-36)/36.

So, v3 = (h-36)/36 ? h-36 = 36v3 ? h = 36(1 + v3) ˜ 36 × 2.732 = 98.35 m.

Option 4 (98 m) is correct.

All the pieces fit.

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