Question

Brianna 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 6700
feet. Brianna initially measures an angle of elevation of 16° to the plane at point A. At
some later time, she measures an angle of elevation of 37° 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.

Answer 1

Using the slope concept, it is found that the distance the plane traveled from point A to point B is of 14,475 feet.

What is a slope?

• The slope is given by the vertical change divided by the horizontal change.

• It's also the tangent of the angle of depression.

At point A:

• Altitude of 6700 feet, which is the vertical change.

• The horizontal position we want to find is $x_A$.

• The angle is of 16º.

Hence:

$\tan{16^{\circ}} = \frac{6700}{x_A}$

$x_A = \frac{6700}{\tan{16^{\circ}}}$

$x_A = 23365.7$

At point B:

• Altitude of 6700 feet, which is the vertical change.

• The horizontal position we want to find is $x_B$.

• The angle is of 37º.

Hence:

$\tan{37^{\circ}} = \frac{6700}{x_B}$

$x_B = \frac{6700}{\tan{37^{\circ}}}$

$x_B = 8891.2$

Then, the distance is of:

$d = x_A - x_B = 23365.7 - 8891.2 \approx 14475$

You can learn more about the slope concept at https://brainly.com/question/26342863