You are looking at a flag pole from 150 ft away and looking up at the top of the flag pole 60 degrees. How tall is the flag pole?

This is a triangle with the ground and the pole as legs, and the view line as hypotenuse. Calculate the pole height h using the sine rule. The angles of the triangle are 90, 60 and 30 (sum must be 180).

The sine rule says that h/sin (60) = 150/sin (30), so h = 150*sin (60) / sin (30) ≈ 259.8