the height of the building

Question

In order to estimate the height of a building, two students stand at a certain distance from the building at street level. From this point, they find the angle of elevation from the street to the top of the building to be 36°. They then move 280 feet closer to the building and find the angle of elevation to be 50°. Assuming that the street is level, estimate the height of the building to the nearest foot.

Answer 1

Here is an outline of the solution:

1. a/sin(A)=b/sin(B)=c/sin(C), where lower case letter is the side length opposite the uppercase angle.
2. Use the law of sines in 1 to calculate one side of the obtuse triangle, which is also the hypotenuse of the inner right triangle.
3. Use law of sines again on the inner right triangle to get the height of the building.