Question

Kayden is trying to find the height of a radio antenna on the roof of a local building. he stands at a horizontal distance of 16 meters from the building. the angle of elevation from his eyes to the roof left bracket(point aaright bracket) is 41degrees ∘ , and the angle of elevation from his eyes to the top of the antenna left bracket(point bbright bracket) is 49degrees ∘ . if his eyes are 1.5 meters from the ground, find the height of the antenna left bracket(the distance from point aa to point bbright bracket). round your answer to the nearest meter if necessary.

Answer 1

To calculate the height of the antenna, use trigonometric functions involving the angles of elevation and the horizontal distance from Kayden to the building. Subtract Kayden's eye level from the results to get the heights from the ground and find the difference between the two heights to get the antenna's height.

Step-by-step explanation:

Kayden is trying to find the height of a radio antenna on the roof of a local building. To calculate the height of the antenna, we can use trigonometry. The height of the point A (roof), given the angle of elevation to point A is 41 degrees and a horizontal distance of 16 meters, can be found using the tangent function:

tangent(41 degrees) = height of A / 16 meters

Similarly, we can find the height of point B (top of the antenna) using the angle of elevation to point B which is 49 degrees:

tangent(49 degrees) = height of B / 16 meters

Once we have these heights, we can subtract the eye level of 1.5 meters from each to obtain the actual heights from the ground, and then find the difference between the two to get the height of the antenna. If necessary, round the final result to the nearest meter.