A plane flying at an altitude of a miles above a radar antenna will pass directly over the radar antenna (see figure).Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. $$a = 8$$ .
(d is positive as the plane approaches the antenna. )
Write d as a function of x.
A)d = 8 csc x
B)d = 8 cot x
C)d = 8 cos x
D)d = 8 tan x
E)d = 8 sin x

Question

A plane flying at an altitude of a miles above a radar antenna will pass directly over the radar antenna (see figure).Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. $$a = 8$$ . ​
(d is positive as the plane approaches the antenna. )
Write d as a function of x.​ 
A)d = 8 csc x 
B)d = 8 cot x 
C)d = 8 cos x 
D)d = 8 tan x 
E)d = 8 sin x

Quizplus · Accepted Answer

Using trigonometry, we have:
tan x = opposite/adjacent = a/d
Therefore, d = a/tan x
Since the altitude of the plane is a, we have: 
d = a/tan x = 8/sin x * cos x/sin x = 8 cot x 
Hence, the answer is choice (B).

A Plane Flying at an Altitude of a Miles Above a=8a = 8a=8

A Plane Flying at an Altitude of a Miles Above $a = 8$