CPM Homework Help : PC3 Problem 10-64

To determine the height, $h$ , of Mount St. Melon in the Cantaloupe Mountains, two angle measurements were taken $1200$ feet apart along a direct line toward the mountain. Using these measurements, calculate the height of the mountain.

Right triangle, vertical leg on right, labeled, h, horizontal leg, divided into 2 parts, left part labeled, 1200 feet, segment connecting point dividing horizontal leg, to vertex opposite horizontal leg, creates 2 triangles, obtuse triangle on left, with left bottom angle labeled 35 degrees, smaller right triangle, on right, with left bottom angle labeled 42 degrees.

Hint:

Label the horizontal leg of the small right triangle $x$ .
Then write two equations using tangent, $x$ , and $h$ .
Solve this system of equations for $h$ .