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प्रश्न
The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
उत्तर
Let the height of the electric pole AD be “h” m
EC = 15 – h m
Let AB be “x”
In the right ∆ABC, tan 60° = `"BC"/"AB"`
`sqrt(3) = 15/x`
x = `15/sqrt(3)`
= `(15 xx sqrt(3))/3`
= `5sqrt(3)`
In the right ∆CDE, tan 30° = `"EC"/"DE"`
`1/sqrt(3) = (15 - "h")/x` ...(1)
Substitute the value of x = `5sqrt(3)` in (1)
`1/sqrt(3) = (15 - "h")/(5sqrt(3))`
⇒ `sqrt(3)(15 - "h") = 5sqrt(3)`
(15 – h) = `(5sqrt(3))/sqrt(3)`
⇒ 15 – h = 5
h = 15 – 5 = 10
∴ Height of the electric pole = 10 m
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