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I really need help with this pre-calculus question that involves angles!?
An airplane is sighted at the same time by two ground observers who are 3 miles apart and in front of the airplane. They report that the angles of elevation are 15 degrees and 21 degrees. How high is the airplane?
a. 2.66 miles
b. 0.78 miles
c. 3.69 miles
d. 1.08 miles
Also, would anyone happen to understand this question?- Find the length of 2v if v = <2, -4, 5>
a. 3 sqrt 5
b. sqrt 13
c. 6 sqrt 5
d. (sqrt 13) / 2
h is height of plane, d is distance (on ground) from close observer to plane, d+3 is distance of other observer. then
h/d = tan 21 and h/(d+3) = tan 15, so
h/tan 15 - 3 = h/tan 21
h[ (tan 21 - tan 15) / (tan 21 • tan 15) ] = 3
h = 3 tan 21 tan 15 / (tan 21 - tan 15)
h = 2.66 mi.
2v = <4, -8, 10> so
| 2v | = √(16 + 64 + 100) = √180 = 6√5
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