Question

An airplane is flying in still air with an airspeed of 240 miles per hour. If it is climbing at an angle 23°, find the rate at which it is gaining altitude. Round your answer to four decimal places.

Answer 1

Answer:

$\sin 23=\mathrm{\frac{Perpendicular}{240}}\\\\0.3907=\mathrm{\frac{Perpendicular}{240}}\\\\ \Rightarrow \mathrm{Gain~in~altitude}=240\times 0.3907 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~=93.78$

Therefore, the rate at which it is gaining altitude 93.78mils per hour

Step-by-step explanation:

Given That,

airspeed of 240 miles per hour.

If it is climbing at an angle 23°,

find the rate at which it is gaining altitude. Round your answer to four decimal places.

Since

$\sin \theta=\mathrm{\frac{Perpendicular}{Hypotenues}}$

In this case the hypotenuse is 240 mph, the perpendicular side is the gain in altitude, 23° is your angle.

$\sin 23=\mathrm{\frac{Perpendicular}{240}}\\\\0.3907=\mathrm{\frac{Perpendicular}{240}}\\\\ \Rightarrow \mathrm{Gain~in~altitude}=240\times 0.3907 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~=93.78$

Therefore, the rate at which it is gaining altitude 93.78mils per hour