Pre Cal Question Need Help

Question

two buildings of equal height are 830 feet apart. And observer on the street between the buildings measures the angles of elevation to the tops of the buildings as 29° and 40°. How high, to the nearest foot, are the buildings?

Answer 1

Let's organize what we know first. (I recommend drawing a picture with labels)

The buildings are equal in height, so lets label the two buildings h.

The space between is 830ft, and the observer is in between. Let's choose one building as a reference point to place our observer. If they are x ft away from one building, how far are they from the other?

We have the angles, so let's label that on the drawing as well.

Now we are left with a picture with 2 triangles and each triangle has 2 labeled sides and 1 labeled angle. See if you can use multiple trig equations to isolate variables and solve for h, the height.