A pilot is flying at 10,000 feet and wants to take the plane up to 20,000 feet over the next 50 miles. What should be his angle of elevation to the nearest tenth?
d = 50mi * 5280Ft/m1 = 264,000 Ft. =
264K.
(0,10k), (264k,20k).
Tan A = (20k-10k)/(264k-0) = 0.037879
A = 2.2 Degrees.
To determine the angle of elevation, we can use trigonometry. We'll need to use the tangent function, which relates the angle of elevation to the opposite side (the change in altitude) and the adjacent side (the horizontal distance traveled). In this case, the opposite side is the change in altitude from 10,000 feet to 20,000 feet (10,000 feet) and the adjacent side is the horizontal distance traveled of 50 miles.
First, let's convert the given units to a common system. We'll convert 50 miles to feet, assuming 1 mile is equal to 5,280 feet:
50 miles * 5,280 feet/mile = 264,000 feet.
Now we can calculate the angle of elevation (θ) using the tangent function:
tan(θ) = opposite/adjacent
tan(θ) = 10,000 feet / 264,000 feet
To find θ, we'll use the inverse tangent (tan⁻¹) function:
θ = tan⁻¹(10,000 feet / 264,000 feet)
Using a scientific calculator or an online calculator, we can find the inverse tangent of 10,000/264,000:
θ ≈ 2.2 degrees.
So, the pilot should have an angle of elevation of approximately 2.2 degrees to ascend from 10,000 feet to 20,000 feet over the next 50 miles.
To find the angle of elevation, we can use the formula:
Angle of elevation = arctan(Change in height / Distance traveled)
In this case, the change in height is 20,000 feet - 10,000 feet = 10,000 feet. The distance traveled is given as 50 miles, but we need to convert it to feet first.
1 mile = 5280 feet
So, 50 miles = 50 * 5280 = 264,000 feet.
Plugging these values into the formula, we have:
Angle of elevation = arctan(10,000 / 264,000)
Using a calculator, the arctan of 10,000 / 264,000 is approximately 2.156 degrees.
Therefore, the pilot should set his angle of elevation to approximately 2.2 degrees to the nearest tenth.