Question

A lamppost tilts toward the sun at a 2 degree angle from the vertical and casts a 25-foot shadow. The angle from the tip of the shadow to the top of the lamp post is 45 degrees. How do you find the length of the lamp post?

Answer 1

Solve triangle

Explanation:

Call A the top of the lamp post, and B the tip of the shadow, and C the bottom of the lamp post. We have : angle C = 92 deg, since the post tilts 2 deg toward the sun.
Angle A = 180 - C - B = 180 - 92 - 45 = 43 deg
Use trig identity to find b, the length b of the lamp post.
`b/sin B = a/sin A -->`b = a(sin B/sin A) = 25(sin 45/sin 43) = #

`b = 25(0.71/0.68) = 26.10`