Question

An airplane is flying at a height of 5 kilometers above the ground. The distance along the ground from the airplane to the airport is 7 kilometers. What is the angle of depression from the airplane to the airport? (Write the answer to the nearest degree.)

Answer 1

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$\large \sf{✟ \: Problem \: ✟} :$

An airplane is flying at a height of 5 kilometers above the ground. The distance along the ground from the airplane to the airport is 7 kilometers. What is the angle of depression from the airplane to the airport? (Write the answer to the nearest degree.)

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$\large \sf{✟ \: Solution \: ✟} :$

✞ Step 1 ✞: Identify what is asked in the problem.

❒ The angle of depression from the airplane to the airport.

✞ Step 2 ✞: Use appropriate trigonometric ratio to solve the problem.

❒ Since the two legs of the right triangle are part of the problem, hence we use tangent ratio:

$\qquad \qquad \bigstar \: \: \boxed{\tt{ \quad \tan A \degree = \frac{5}{7} \quad}}$

✞ Step 3 ✞: Solution and interpretation.

$: \qquad \large \implies \tt{ \tan A = \frac{5}{7} }$

$: \qquad \large \implies \tt{A = \tan^{ - 1}(\frac{5}{7} )}$

$: \qquad \large \implies \tt{A = 35.54 \approx \pmb{36 \degree}}$

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$\large \sf{✟ \: Answer \: ✟} :$

Hence, the angle of depression from the airplane to the airport is approximately 36°.

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$\large \bold{✰ \: MrHarold \: ࿐}$