Question

This a problem I need help with. A vertical ple stands by a road that is inclined 10 degrees to the horizontal. When the angle of elevation of the sun is 23 degrees, the pole casts a shadow 38 ft long directly downhill along the road. How long is the pole?

Answer 1

Inclined 10 degrees to the horizontal? That is hardly vertical. But at any rate, you know the angle of the shadow(sunlight) to the horizontal, the length and the base angle.
ASA you can use the law of sines, which I recommend.