At takeoff, a plan flies at an angle of 10 debrees with the runway. After it has traveled a ground distance of 2,800 feet, find the vertical distance the plane has gained from takeoff. Round your answer to the nearest foot
if the plane has reached height h,
h/2800 = tan 10°
now plug and chug to get h=494
To find the vertical distance the plane has gained, we can use trigonometry. Specifically, we can use the sine function.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the hypotenuse is the ground distance traveled by the plane, which is 2,800 feet.
First, we need to find the length of the side opposite the angle of 10 degrees. We can use the sine function to do this:
sin(10 degrees) = opposite side / hypotenuse
Plugging in the known values, we have:
sin(10 degrees) = opposite side / 2,800 feet
Next, we can rearrange the equation to solve for the opposite side:
opposite side = sin(10 degrees) * 2,800 feet
Calculating this expression, we find:
opposite side ≈ 481.7 feet
Therefore, the vertical distance the plane has gained from takeoff is approximately 481.7 feet (rounded to the nearest foot).