Solve Example 6 using right triangle geometry. Comment on which solution, using the Law of Sines or using right triangles, you prefer. Give reasons.

Data from example 6

To measure the height of a mountain, a surveyor takes two sightings of the peak at a distance 900 meters apart on a direct line to the mountain. See Figure 31(a). The first observation results in an angle of elevation of 47°, and the second results in an angle of elevation of 35°. If the transit is 2 meters high, what is the height h of the mountain?

2 m 35 900 m 47 (a) h