Question

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? `(sqrt(3) = 1.732)`

Answer 1

Let the height of the window FE be “h” m

Let FC be “x” m

∴ EC = (h + x)m

In the right ∆CDF, tan 45° = `"CE"/"CD"`

1 = `x/5`

⇒ x = 5

In the right ∆CDE, tan 60° = `"CE"/"CD"`

`sqrt(3) = (x + "h")/5`

⇒ x + h = `5sqrt(3)`

5 + h =  `5sqrt(3)`   ...(substitute the value of x)

h = `5sqrt(3) - 5`

= 5 × 1.732 – 5

= 8.66 – 5

= 3.66

∴ Height of the window = 3.66 m