From a hot air balloon, Sean looks through an angle of depression of 35 degrees to see LeAnn on the on the ground. If Sean and LeAnn are 500 ft. apart by the line of sight distance, to the nearest foot, how far is Sean off the ground?
I used 500(cos55)
I believe that's right; or 500*sin(35)
good, carry on
correct.
To solve this problem, you can use trigonometry. Let's denote the height of the hot air balloon as "x".
Given that Sean is looking through an angle of depression of 35 degrees, we can infer that the angle formed between the line of sight and the ground is also 35 degrees (since the sum of angles in a triangle is 180 degrees).
Using the given information, we have an adjacent side (the distance between Sean and LeAnn) of 500 ft and an angle of 35 degrees. We need to find the opposite side, which represents the height of Sean above the ground.
You correctly used the cosine function to find the height:
cos(35) = x / 500
To find x, rearrange the equation:
x = 500 * cos(35)
Evaluating this expression using a calculator, we get:
x ≈ 408.04 ft
Therefore, Sean is approximately 408 feet off the ground.