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Question
A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)
Solution
Let the height of the statue be h m
Let AD be x
∴ EC = h – x
In the right ∆ABD,
tan 34° = `"AD"/"AB"`
0.6745 = `x/35`
∴ x = 0.6745 × 35
⇒ x = 23.61 m
In the right ∆DEC
⇒ tan 24° = `"EC"/"DE"`
0.4452 = `("h" - x)/35`
⇒ h – x = 0.4452 × 35
h – 23.61 = 15.58
⇒ h = 15.58 + 23.61
= 39.19 m
Height of the statue = 39.19 m
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