A spotlight on the ground 3 feet away from a 5 feet tall man cast a 15 feet shadow on a wall 6 feet away from the man. Find the angle in which light is placed?
At an angle of
feet. So the triangles formed
are similar triangles.Let angle cast by the light be
Both the man and the shadow form proportional right triangles, so we can really use either one to solve your problem. Let's use the man.
The triangle is formed by the spotlight, the man's feet on the ground and his head (It's helpful to draw a picture). If we're looking at the light as an angle (
It also works if you use the larger triangle (spotlight, base of wall, top of shadow)
Hope that helps.