CPM Homework Help : PC Problem 3-64

To find 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, find 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.

Solution Steps:

1. Find angle $ABD$ by subtracting $42$ from $180^\circ$ .
2. Now find angle $ADB$ . You know the sum of the angles of a triangle $= 180^\circ$ .
3. Use the Law of Sines to find length $BD$ .
4. Use the $\sin42^\circ$ and $BD$ to find $h$ .

Added to triangles, horizontal leg, left vertex labeled, A, right angle vertex labeled c, point between labeled, b, top vertex labeled, d.