The statue of Liberty stands on a 150ft. pedestal. From a point 250ft. from the base of the pedestal, the angle of elevation to the top of Liberty’s torch is 50o. Find the height of the Statue of Liberty.

The height of the statue of liberty is 147.938 ft

Step-by-step explanation:

The  statue of liberty stands on a pedestal of 150 ft. From a point 250 ft from the base of the pedestal, the angle of elevation to the top of Liberty’s torch is 50°.

This represents a right angle triangle with a total height = (height of the statue) + height of the pedestal

let a be the height of the statue, Therefore the total height = (a + 150) ft

The triangle has a base length of 250 ft and an angle of elevation of 50°.

From this, since:

tan(Θ) = opposite/adjacent

where the opposite side to the angle Θ is (a + 150) ft and the adjacent to the angle Θ is 250 ft and Θ = 50°

⇒ tan(Θ) = opposite/adjacent

∴ tan(50) = (a + 150)/250

1.192 = (a + 150)/250

1.192 × 250 = (a + 150)

(a + 150) = 297.938

a = 297.938 - 150 = 147.938

a = 147.938 ft

The height of the statue of liberty is 147.938 ft