Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.

What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

A) 3.0 yards

B) 3.2 yards

C) 3.8 yards

D) 4.4 yards

Question

Elisha Pena

Mathematics

24 April, 04:16

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.

What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

A) 3.0 yards

B) 3.2 yards

C) 3.8 yards

D) 4.4 yards

+4

Answers (1)

Know the Answer?

Allie Duncan · Answer 1

Let the height of the three be h and the distance between student A and the tree be x, then

tan 57 = h/x

x = h/tan 57

tan 46 = h / (x + 1)

x + 1 = h/tan 46

h/tan 57 + 1 = h / tan 46

h / tan 46 - h / tan 57 = 1

h (tan 57 - tan 46) = tan 46 tan 57

h = tan 46 tan 57 / (tan 57 - tan 46) = 3.2 yards