Question

standing on the street, the top of a building has an angle of elevation of 20 degrees. You walk 300 feet directly toward the building, and the angle of elevation is now 25 degrees. How tall is the building

Answer 1

The value of height of the building h = 509.2 feet

Explanation:

From the Δ A B C

`\tan 25 = (h)/(y)`

⇒ h = y
`\tan 25`° ------- (1)

From Δ A B D

`\tan 20 = (h)/(y + 300)`

⇒ h = ( y + 300 )
`\tan20`° ------- (2)

Equation 1 = Equation 2

⇒ y
`\tan 25`° = ( y + 300 )
`\tan20`°

⇒ 0.46 y = 0.36 y + 109.2

⇒ 0.1 y = 109.2

⇒ y = 1092 feet

Put this value of y in equation ( 1 ) we get,

⇒ h = 1092 × tan 25°

⇒ h = 509.2 feet

This is the value of height of the building.