Question

Angel is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 21 meters from the building. The angle of elevation from his eyes to the roof (point A) is 38°, and the angle of elevation from his eyes to the top of the antenna (point B) is 46°. If his eyes are 1.66 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest tenth of a meter if necessary.

Answer 1

First, we need to find the height of point A, which is where Angel is standing. We can use the tangent function to do this:

tan(38°) = height of point A / 21 meters

height of point A = 21 meters * tan(38°) = 14.1 meters

Next, we need to find the distance from point A to point B. We can use the tangent function again, this time with the angle of elevation from point A to point B:

tan(46°) = distance from point A to point B / 21 meters

distance from point A to point B = 21 meters * tan(46°) = 20.8 meters

Finally, we can add the height of point A and the distance from point A to point B to get the height of the antenna:

height of antenna = height of point A + distance from point A to point B + height of Angel's eyes

height of antenna = 14.1 meters + 20.8 meters + 1.66 meters = 36.56 meters

Therefore, the height of the antenna is approximately 36.6 meters.