A pilot sees a guy at an angle of depression of 50 degrees. If the pilot is 200 degrees from the guy, how high is the pilot?
Would it be sin(50) x 200?
correct
To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle of depression is equal to the height of the observer divided by the distance from the observer to the object of interest.
Here's how you can find the height of the pilot:
1. First, draw a diagram to visualize the situation. Label the angle of depression as 50 degrees and the distance between the pilot and the guy as 200 meters.
2. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the opposite side is the pilot's height, and the adjacent side is the distance between the pilot and the guy.
3. Using the tangent function, we can write the equation as follows:
tan(50) = height of the pilot / 200
4. Now, to find the height of the pilot, we can rearrange the equation:
height of the pilot = tan(50) * 200
5. Finally, calculate the height of the pilot by multiplying the tangent of 50 degrees by 200:
height of the pilot = tan(50) * 200
By plugging in the values and evaluating the expression, you'll find the height of the pilot.