Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# 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, w - Mathematics

Sum

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)

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 6 Trigonometry
Exercise 6.2 | Q 3 | Page 257