Use the scenario to answer the question.
Sierra is climbing a rock wall and has reached a height of 6 meters. Her belayer is standing on the ground 5.5 meters away from the base of the rock wall. What is the angle of depression from Sierra to her belayer? Round your answer to the nearest whole number.
The angle of depression is __________°.
I think it is 47 degrees. Am I correct?
47 degrees is the correct answer
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle formed between the line of sight from an elevated point to a point below it and the horizontal line. In this scenario, Sierra is at the top of the rock wall, and her belayer is standing on the ground.
To find the angle of depression, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the rock wall (6 meters), and the adjacent side is the horizontal distance between Sierra and her belayer (5.5 meters).
So, the formula for the tangent of the angle of depression is:
tangent(angle) = opposite/adjacent
tangent(angle) = 6/5.5
Now, we can use a calculator to find the value of the tangent. Plug in the values:
tangent(angle) ≈ 1.09
To find the angle itself, we need to take the arctangent or inverse tangent of 1.09. Using the inverse tangent function on a calculator, we can find the angle:
angle ≈ 47.19 degrees
Rounding to the nearest whole number, the angle of depression from Sierra to her belayer is approximately 47 degrees.
So yes, you are correct! The angle of depression is 47 degrees.
tan theta = 6/5 = 1.2
so
theta = 50.2