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Whitepunk [10]
4 years ago
11

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the an

gle 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
Mathematics
2 answers:
Ahat [919]4 years ago
8 0

Answer:

3.2 yards

Step- by-step explanation:

FromTheMoon [43]4 years ago
3 0
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
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