# Two hotels stand 25 m apart. One of them is 70 m high and the angle of depression of the top of other as observed from the top of this hotel is 45°. Height of the other hotel is:

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DSSSB TGT Maths Male Subject Concerned - 23 Sep 2018 Shift 2
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1. 46 m
2. 44 m
3. 43 m
4. 45 m

Option 4 : 45 m

## Detailed Solution

Given:

Two hotels stand 25 m apart. One of them is 70 m high and the angle of depression of the top of the other as observed from the top of this hotel is 45°.

Formula used:

For a right angle triangle ABC,

$$tanθ = \frac{perpendicular}{base} = \frac{BC}{AB}$$

For θ = 45, tanθ = 1

Calculation:

In Δ ABE,

tan 45° = $$\frac{70 - h}{25}$$

⇒ $$\frac{70 - h}{25}$$ = 1

⇒ 70 - h =  25

⇒ h = 70 - 25 = 45h

⇒ h = 45m

$$sin\theta = \frac{perpendicular}{hypoteneous}$$
$$Cos\theta = \frac{base}{hypoteneous}$$
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