Question

A plane rises from take-off and flies at an angle of 10 degrees with the horizontal runway. When it has gained 500 feet in altitude, find the distance, to the nearest foot, the plane has flown.

Answer 1

To calculate the distance the plane has flown with a 10-degree angle of ascent and a 500-foot altitude gain, we use the tangent function in trigonometry. The plane has flown approximately 2839 feet to the nearest foot.

Step-by-step explanation:

The distance a plane has flown given a 10-degree angle of ascent and an altitude gain of 500 feet. This is a trigonometry problem that involves finding the hypotenuse of a right triangle where the opposite side is known. Using the tangent function which is the ratio of the opposite side over the adjacent side (tan(θ) = opposite/adjacent), we can rearrange the formula to solve for the adjacent side, which represents the distance flown.

Here's the calculation:

• tan(10°) = 500/adjacent
• adjacent = 500/tan(10°)
• adjacent ≈ 500/0.1763
• adjacent ≈ 2839 feet

To the nearest foot, the plane has flown approximately 2839 feet.

Answer 2

To find the distance the plane has flown at a 10 degree angle of ascent, we can use trigonometry to calculate the base side of the right triangle formed by altitude gained and distance flown. The tangent function can be used to relate the altitude gained to the distance flown.

Step-by-step explanation:

To find the distance the plane has flown, we can use trigonometry and the concept of a right triangle. Since the angle of elevation is given as 10 degrees, we can consider the altitude gained as the height side of the triangle. Let's assume that the distance flown is the base side of the triangle. Using trigonometric functions, we can determine the length of the base side. In this case, the tangent function will be appropriate.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the altitude gained (500 feet) and the adjacent side is the distance flown. Therefore, we can write:

Tan(10 degrees) = 500 / x, where x is the distance flown.

To find x, we can rearrange the equation as follows:

x = 500 / Tan(10 degrees)

Using a calculator, we can find the value of Tan(10 degrees) to be approximately 0.176327 and substitute it into the equation:

x = 500 / 0.176327

x ≈ 2837.6 feet