110k views
5 votes
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.

1 Answer

1 vote
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.
User Chris Frost
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.