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(Show full work please) Carter spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 7250 feet.
Carter initially measures an angle of elevation of 16 to the plane at point A. At some
later time, he measures an angle of elevation of 26° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary

Respuesta :

LammettHash

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

Ver imagen LammettHash

The distance the plane traveled from point A to point B is 10,433 ft.

We have given that,

Carter spots an airplane on the radar that is currently approaching in a straight line, and that will fly directly overhead.

The plane maintains a constant altitude of 7250 feet.

In the larger triangle,tan(16°) = (7250 ft) / (x + y)and in the smaller triangle,

What is the tan ratio?

[tex]tan(\ theta)=\frac{\\opposite \side }{hypotenouse}[/tex]tan(26°) = (7250 ft) / y

we have 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

Therefore the distance the plane traveled from point A to point B is 10,433 ft.

To learn more about altitude visit:

https://brainly.com/question/22736499

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