Question

as observed from a point on ground,the angle of elevation of top of house is 45 degree. find height of house

Answer 1

Hey there !

Let us assume that the point of observation is 'x' meters away from the house and the height of the house to be 'h'.

Now the angle of elevation is 45°. So if we assume the height of house to opposite side of a triangle and the distance between house and point of observation to be adjacent side of the triangle then it is a right angle triangle that is formed as House is perpendicular to the ground.

So applying trigonometry we get,

Tan Ф = Opposite side / Adjacent side

=> Tan 45° = Height of House / Distance ( x )

=> 1 = Height of house / Distance ( x )

=> Height of House = Distance ( x )

So the height of the house is same as that of the distance 'x' present between the point of observation to the foot of the house.

Hope my answer helped !