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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)`
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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