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

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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

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APPEARS IN

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