Final answer:
The horizontal distance traveled by an airplane climbing at a 27-degree angle to an altitude of 600 feet can be calculated using the cosine function of trigonometry, by dividing the altitude by the cosine of the angle in radians.
Step-by-step explanation:
The student's question revolves around calculating the horizontal distance traveled by an airplane that climbs at a 27 degrees angle to reach an altitude of 600 feet. To solve this, we use trigonometric functions, specifically the cosine function, since we are given the opposite side (altitude) and we need to find the adjacent side (distance traveled).
To find the horizontal distance (d), we use the formula:
d = altitude / cos(angle)
First, we must convert the angle from degrees to radians, because trigonometric functions typically require the angle to be in radians:
angle in radians = angle in degrees × (π / 180)
27 degrees in radians = 27 × (π / 180)
We can then plug in the altitude and the angle in radians into the formula:
d = 600 ft / cos(27 degrees in radians)
By performing the calculation, we obtain the distance (d) that the airplane has traveled horizontally.