Answer:
The height of the statue of liberty is 147.938 ft
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