(Show full work please) Carter spots an airplane on radar that is currently approaching in a straight line, and
1 answer:
Consult the attached diagram.
In the larger triangle,
tan(16°) = (7250 ft) / (<em>x</em> + <em>y</em>)
and in the smaller triangle,
tan(26°) = (7250 ft) / <em>y</em>
You want to solve for <em>x</em>.
From the first equation (I'm ignoring units from here on, all distances are measured in ft), you have
(<em>x</em> + <em>y</em>) tan(16°) = 7250
<em>x</em> tan(16°) + <em>y</em> tan(16°) = 7250
<em>x</em> tan(16°) = 7250 - <em>y</em> tan(16°)
<em>x</em> = 7250 cot(16°) - <em>y</em>
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From the second equation,
<em>y</em> = 7250 cot(26°)
Solving for <em>x</em> gives
<em>x</em> = 7250 cot(16°) - 7250 cot(26°)
<em>x</em> = 7250 (cot(16°) - cot(26°))
<em>x</em> ≈ 10,433 ft
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