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

Answer:

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

Step-by-step 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'

$\frac{x}{b}=tan 45$ =1

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

total height of the building is given as 12m

  x + y + 2=12

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

$\frac{x+y}{b} =\frac{x+y}{x }$  = tan 60

$\frac{10}{x} = \sqrt{3}$

x = $\frac{10}{\sqrt{3} }$  ≈ 5.77m

y = 10 -   $\frac{10}{\sqrt{3} }$

y= 10(1-$\frac{1}{\sqrt{3} }$ ) ≈ 4.23m

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