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Xochitl 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 7425 feet. Xochitl initially measures an angle of elevation of
19^(@) 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.

Xochitl 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 $7425$ feet. Xochitl initially measures an angle of elevation of $19^{\circ}$ to the plane at point $A$ . At some later time, she measures an angle of elevation of $37^{\circ}$ 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.

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Add and subtract integers: word problems

Full solution

Q. Xochitl 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

7425

feet. Xochitl initially measures an angle of elevation of

19^{\circ}

to the plane at point

A

. At some later time, she measures an angle of elevation of

37^{\circ}

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.

Identify Problem and Values: Step $1$ : Identify the problem and known values. $\newline$ We know the altitude of the plane is $7425$ feet, and the angles of elevation from points A and B are $19$ degrees and $37$ degrees, respectively.
Use Tangent Function: Step $2$ : Use the tangent function to find the distances from Xochitl to the plane at points A and B. $\newline$ For point A: $\tan(19°) = \frac{7425}{\text{distance}_A}$ $\newline$ $\text{distance}_A = \frac{7425}{\tan(19°)}$ $\newline$ $\text{distance}_A \approx \frac{7425}{0.344} = 21599$ feet (approximately) $\newline$ For point B: $\tan(37°) = \frac{7425}{\text{distance}_B}$ $\newline$ $\text{distance}_B = \frac{7425}{\tan(37°)}$ $\newline$ $\text{distance}_B \approx \frac{7425}{0.753} = 9867$ feet (approximately)
Calculate Distance Traveled: Step $3$ : Calculate the distance the plane traveled from point A to point B. $\newline$ Distance traveled = $\text{distance}_A - \text{distance}_B$ $\newline$ Distance traveled = $21599$ feet - $9867$ feet $\newline$ Distance traveled = $11732$ feet

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