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.

Identify Problem and Values: Step 1: Identify the problem and known values. 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. For point A: tan(19°) = 7425 / distance_A distance_A = 7425 / tan(19°) distance_A ≈ 7425 / 0.344 = 21599 feet (approximately) For point B: tan(37°) = 7425 / distance_B distance_B = 7425 / tan(37°) distance_B ≈ 7425 / 0.753 = 9867 feet (approximately) Calculate Distance Traveled: Step 3: Calculate the distance the plane traveled from point A to point B. Distance traveled = distance_A - distance_B Distance traveled = 21599 feet - 9867 feet Distance traveled = 11732 feet

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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 $19^{\circ}$ 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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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