Answer :
The horizontal distance traveled by an airplane climbing at a 12-degree angle to an altitude of 500 feet is approximately 2352 feet, by using the cosine function of trigonometry. Option A
To find the horizontal distance traveled by an airplane that climbs at an angle of 12 degrees with the ground until it reaches an altitude of 500 feet, we use trigonometric functions. Specifically, we will use the cosine function, since we are looking for the adjacent side of a right-angled triangle (the horizontal distance), while we know the angle and the opposite side (the altitude).
The formula we use, based on trigonometric definitions, is:
Cosine(angle) = Adjacent side (horizontal distance) / Hypotenuse
Here, the hypotenuse is the slant distance of the climb, but we only need to find the adjacent side (horizontal distance). We can rearrange the formula to solve for the horizontal distance:
Horizontal distance = Altitude / Cosine(angle)
Plugging in our known values:
Horizontal distance = 500 feet / Cosine(12 degrees)
Using a calculator or a trigonometry table:
Horizontal distance
gx 500 feet / ~0.9781
The horizontal distance is approximately 2352 feet, which makes option (a) the correct answer.
