can anyone help my answer this question my answer was 4,080 however it was wrong

Question

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 4.7 mi apart, to be 36° and 47°, as shown in the figure.

4.7 mi36°47°BA

What is the elevation of the plane in feet? Give your answer to the nearest whole number.

Answer 1

You need to draw a figure.

Then use the geometry of parallel lines to find an obtuse triangle with angles of 11 degrees and 36 degrees.

Use the law of sines to find the 2nd leg of that obtuse triangle; this side is also the hypotenuse of a right triangle which includes the required altitude as a side and then a simple trig calculation will get you the altitude.

Answer 2

The angle of elevation corresponding to the angle of

depression of 47 degrees is 90- 47= 43 degrees.

The angle of elevation corresponding to the angle of

depression of 36 degrees is 90- 36 = 54 degrees.

DEGREE AND THE 47 DEGREE ANGLES OF

DEPRESSION, OR 11 DEGREES.

THAT IS ACROSS FROM THE SIDE GIVEN AS

4.6 MILES. THE LONGER OF THE TWO

LINES-OF-SIGHTS COMING FROM THE AIRPLANE

IS ACROSS FROM AN ANGLE = 180 - 11 - 36

= 133 DEGREES.

X=SIN(133)*(4.6 MILES)/SIN(11) =

17.6313858831 MILES

HEIGHT OF THE AIRPLANE / HYPOTENUSE =

OPPOSITE / HYPOTENUSE = SIN(36 DEGREES)

SO HEIGHT = HYPOTENUSE * SIN(36 DEGREES) =

10.3634685996 MILES

SORRY! THIS SYSTEM WOULD NOT ALLOW ME TO POST AN EXPLANATORY DIAGRAM.