The Statue of Liberty is 305 ft tall, from the ground to the top of her torch. If you stood 85 ft away and used a clinometer to view the top of the statue, what would the clinometer read?
16.2°
73.8°
74.40
15.6°
To determine the reading on the clinometer, we can use trigonometry to calculate the angle of elevation.
Let's consider a right triangle, where the height of the Statue of Liberty is the opposite side, the distance from the observer to the statue is the adjacent side, and the angle of elevation is the angle measure we want to find.
The tangent function can be used to relate these sides and angles in a right triangle:
tan(angle) = opposite / adjacent
In this case, we want to find the angle, so we can rearrange the formula to solve for the angle:
angle = arctan(opposite / adjacent)
Plugging in the values:
opposite = 305 ft
adjacent = 85 ft
angle = arctan(305 / 85) = 74.4866...
Rounded to one decimal place, the clinometer reading would be approximately 74.4°.
So the correct answer is 74.40°.