Question

an airplane pilot wishes to make his approach to an airstrip at an angle of 15° with the horizontal. if he is flying at an altitude of 2500 feet, approximately how far from the airstrip should he begin his descent?

Explanation:

Step1: <Use trigonometric ratio>

Let the horizontal distance from the airstrip be \(x\). We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 15^{\circ}\) and the opposite side (altitude) \(y = 2500\) feet. So, \(\tan15^{\circ}=\frac{2500}{x}\).

Step2: <Find value of \(\tan15^{\circ}\)>

We know that \(\tan15^{\circ}=2 - \sqrt{3}\approx0.2679\).

Step3: <Solve for \(x\)>

From \(\tan15^{\circ}=\frac{2500}{x}\), we get \(x=\frac{2500}{\tan15^{\circ}}\). Substituting \(\tan15^{\circ}\approx0.2679\), we have \(x=\frac{2500}{0.2679}\approx9330\) feet.

Answer:

\(9330\) feet