Question

(Show full work please) Carter spots an airplane on radar that is currently approaching in a straight line, and

Answer 1

Consult the attached diagram.

In the larger triangle,

tan(16°) = (7250 ft) / (x + y)

and in the smaller triangle,

tan(26°) = (7250 ft) / y

You want to solve for x.

From the first equation (I'm ignoring units from here on, all distances are measured in ft), you have

(x + y) tan(16°) = 7250

x tan(16°) + y tan(16°) = 7250

x tan(16°) = 7250 - y tan(16°)

x = 7250 cot(16°) - y

From the second equation,

y = 7250 cot(26°)

Solving for x gives

x = 7250 cot(16°) - 7250 cot(26°)

x = 7250 (cot(16°) - cot(26°))

x ≈ 10,433 ft