A pole at a right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. The pole's shadow is 16 meters long and points up the slope. The angle of elevation from the tip of the shadow to the sun is 20 degrees.

Question

A pole at a right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal.  The pole's shadow is 16 meters long and points up the slope.  The angle of elevation from the tip of the shadow to the sun is 20 degrees.

What is the height of the pole?

bobpursley · Answer

You have two angles in the triangle (draw the figure), and one side. With two angles, you can figure the last angle. I would use the law of sines, but you could use the law of cosines.