The rattler roller coaster is 66 ft tall. if you are at the top of the roller coaster and your friend Larry is on the ground 35 ft away from the base of the coaster what is the angle of depression from the top of the roller coaster to the spot where Larry is standing? round to the nearest hundredth
A 125.46
B 16.26
C62.06
D 116.36
What was the answer that you chose? I'm asking so people don't just give you the answer and we can check it(:
I do not know.
To find the angle of depression from the top of the roller coaster to the spot where Larry is standing, we can use basic trigonometric principles.
First, let's define the terms involved:
- Height of the roller coaster (opposite side) = 66 ft
- Horizontal distance between the base of the coaster and Larry's position (adjacent side) = 35 ft
The tangent function relates the opposite and adjacent sides of a right triangle:
tan(theta) = opposite / adjacent
In this case, the opposite side is the height of the roller coaster, and the adjacent side is the horizontal distance between the base of the coaster and Larry's position.
So, tan(theta) = 66 / 35
To find the angle (theta) itself, we need to take the inverse tangent (arctan) of both sides:
theta = arctan(66 / 35)
Using a calculator, we find:
theta ≈ 62.06 degrees
Therefore, the angle of depression from the top of the roller coaster to the spot where Larry is standing is approximately 62.06 degrees.
The correct answer is option C: 62.06.