Question

use the image to answer the question. a plane is taking off at a 15° angle from a horizontal runway. when the altitude of the plane is 250 feet, apply trigonometric functions and the pythagorean theorem to find x, the horizontal distance the plane has flown. round the answer to the nearest whole number. (1 point) x = \square feet

Explanation:

Step1: Identify trigonometric relation

We have a right triangle where the opposite side to the \(15^\circ\) angle is \(250\) feet (altitude), and \(x\) is the adjacent side (horizontal distance). We use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan(15^\circ)=\frac{250}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{250}{\tan(15^\circ)}\). Calculate \(\tan(15^\circ)\approx0.2679\). Then \(x=\frac{250}{0.2679}\approx933\).

Answer:

\(933\)