The Statue of Liberty is 305 ft tall, from the ground to the top of her torch. If you stood 120 ft away and used a clinometer to view the top of the statue, what would the clinometer read?
a. 68.5°
c. 23.2°
b. 21.5°
d. 66.8°
To solve this problem, we can use the tangent function.
Let x be the angle that the clinometer would read.
The height of the Statue of Liberty can be represented by the opposite side of the triangle, which is 305 ft.
The distance from the observer to the statue can be represented by the adjacent side of the triangle, which is 120 ft.
Using the tangent function, we have:
tan(x) = opposite/adjacent
tan(x) = 305/120
Now we can find the value of x by taking the inverse tangent (arctan) of both sides:
x = arctan(305/120)
Using a calculator, we find that x is approximately 68.5°.
Therefore, the clinometer would read approximately 68.5°.
The correct answer is a. 68.5°.