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 (point A) is 41°, and the angle of elevation from
his eyes to the top of the antenna (point B) is 49°. If his eyes are 1.5 meters from the
ground, find the height of the antenna (the distance from point A to point B).
Round your answer to the nearest meter if necessary.

Answer 1

To find the height of the antenna, we can use trigonometry. The height of the antenna can be calculated by setting up two right triangles and using the tangent function. First, we find the height of the building, and then we calculate the height of the antenna.

Step-by-step explanation:

To find the height of the antenna, we can use trigonometry. Let the height of the antenna be h meters. Using the angle of elevation from Kayden's eyes to the roof and the distance between Kayden and the building, we can setup a right triangle. The opposite side of the triangle is the height of the building (16 meters) and the adjacent side is the distance from Kayden to the building. Using the tangent function, we have:

tan(41°) = height of the building / 16

Solving for the height of the building, we get:

height of the building = 16 * tan(41°)

Next, we can setup another triangle using the angle of elevation from Kayden's eyes to the top of the antenna and the distance between Kayden and the building. The opposite side of the triangle is the height of the building plus the height of the antenna (h + height of the building) and the adjacent side is the distance from Kayden to the building. Using the tangent function again, we have:

tan(49°) = (h + height of the building) / 16

Solving for h, we get:

h = 16 * tan(49°) - height of the building

Substituting the value of height of the building, we can calculate the height of the antenna.