Question

a plane rises from take - off and flies at an angle of 13° with the horizontal runway. when it has gained 650 feet, find the distance, to the nearest foot, the plane has flown.
the plane has flown approximately □ feet.
(do not round until the final answer. then round to the nearest foot as needed)

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the opposite side to the \(13^\circ\) angle is 650 feet (the gain in height), and the hypotenuse is the distance the plane has flown (\(x\)). The sine function relates the opposite side and the hypotenuse: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(13^\circ)=\frac{650}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{650}{\sin(13^\circ)}\).

Step3: Calculate the value

First, find \(\sin(13^\circ)\) using a calculator. \(\sin(13^\circ)\approx0.22495\). Then, \(x=\frac{650}{0.22495}\approx2889.4\). Rounding to the nearest foot gives \(x\approx2889\).

Answer:

2889