Find the distance between house and the temple if the heights of house

Pathshala Nepal

3 years ago

The heights of house and temple are 13 m and 25 m respectively. If a man observes the roof of a temple he finds the angle of depression 45°, find the distance between the house and the temple.

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Pathshala Nepal

3 years ago

Solution:

Let,

AB be the height of the house,
CD be the height of the temple,
AF = BD is the distance between house and temple,
∠ECA be the roof of the house from the roof of the temple.

Then,

AB = FD = 13 m,
CD = 25 m,
∠ECA = ∠CAF = 45°,
AF = BD = ?

Here, CF = CD - FD
= 25 m - 13 m
= 12 m

Now, in the right angled triangle ΔCFA,

tan(45°) = CF/AF
Or, 1 = 12m/BD
Or, BD = 12 m

∴ The distance between the house and the temple is BD = 12 m

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