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)

Answer 1

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