A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island directly in front of th

Question

OLga [1]

3 years ago

11

A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island directly in front of th

e balloon to be 75.8° and 15.6°. What is the length of the island to the nearest tenth of a mile?

Mathematics

1 answer:

saul85 [17] · Answer 1 · 2022-03-19T12:24:55+03:00

saul85 [17]3 years ago

3 0

The length of the island will be given as follows:
tan θ=opposite/adjacent
thus:
tan75.8= 3000/a1
a1=3000tan75.8
a1=11855.885 ft

also:
tan15.6=3000/a2
a2=3000tan15.6
a2=837.62 ft
Thus the length of the island will be:
11855.885-837.615
=11,018.24 ft