Question

A man 2 m high observes the angles of elevation of the rops of house and a window on its sode are 45 and 60 respectively. If the top is at height of 12m above the ground , find the height.

Answer 1

The height of the window = x + 2 = 4.23 + 2= 6.23m

Explanation:

The angle of elevation of the top of the house and the window is 60 and 45 degree.

We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.

• draw a horizontal line along the height of a man so that it touches building at height 2m
• till the window height we assume its height as 'x' from the man's height.
• distance till the top from the window will be 'y'

we don't know the distance between man and the building let it be 'b'

`(x)/(b)=tan 45` =1

x=b .............(1)

total height of the building is given as 12m

x + y + 2=12

x + y = 10 .....................(2)

`(x+y)/(b) =(x+y)/(x )` = tan 60

`(10)/(x) = √(3)`

x =
`(10)/(√(3) )` ≈ 5.77m

y = 10 -
`(10)/(√(3) )`

y= 10(1-
`(1)/(√(3) )` ) ≈ 4.23m

The height of the window = x + 2 = 4.23 + 2= 6.23m