Question

a plane rises from take - off and flies at an angle of 14° with the horizontal runway. when it has gained 850 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 trigonometric ratio

We have a right triangle where the opposite side to the $14^\circ$ angle is 850 ft, and we need the hypotenuse (distance flown, $c$). Use sine:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(14^\circ) = \frac{850}{c}$

Step3: Solve for $c$

Rearrange to isolate $c$:
$c = \frac{850}{\sin(14^\circ)}$
Calculate $\sin(14^\circ) \approx 0.2419$, then:
$c \approx \frac{850}{0.2419}$

Step4: Compute final value

$c \approx 3513.85$
Round to nearest foot.

Answer:

3514