16. The drawing shows a person looking at a building on top of which an antenna is mounted. The horizontal distance between the person’s eyes and the building is 85.0 m. In part a the person is looking at the base of the antenna, and his line of sight makes an angle of 35.0° with the horizontal. In part b the person is looking at the top of the antenna, and his line of sight makes an angle of 38.0° with the horizontal. How tall is the antenna?

Let’s call the height of the Antenna, A. Let’s call the height of the building above the eyes, B. For the eyes let’s call that height E.

Now we have two triangles. The left one (a) can be expressed by the following Tangent relationship

And the right one (b) can be expressed by

Solve these two relationships as follows

And

We can find A by doing the following

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This page last updated on January 11, 2020