Question

a plane rises from take - off and flies at an angle of ( 5^{circ} ) with the horizontal runway. when it has gained 750 feet, find the distance, to the nearest foot, the plane has flown.
the plane has flown approximately ( square ) 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 \(5^{\circ}\) angle is 750 feet (the height gained), and the hypotenuse \(c\) is the distance the plane has flown. We use the sine function, which is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(5^{\circ})=\frac{750}{c}\).

Step2: Solve for \(c\)

Rearranging the formula for \(c\), we get \(c = \frac{750}{\sin(5^{\circ})}\).

Step3: Calculate the value

First, find the value of \(\sin(5^{\circ})\) using a calculator. \(\sin(5^{\circ})\approx0.08715574275\). Then, \(c=\frac{750}{0.08715574275}\approx8605.22\). Rounding to the nearest foot, we get \(c\approx8605\).

Answer:

8605