An airplane is flying 100 km north and 185 km west of an airport. It is flying at a height of 7 km
A) what is the straight long distance to the airport?
B) what is the angle of elevation of the airplane, from the point of view of the airport?
A √(100^2+185^2+7^2) = 210.4 km
B tanθ = 7/√(100^2+185^2)
so, θ=1.9°
To find the straight-line distance to the airport, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the straight-line distance of the airplane to the airport is the hypotenuse.
A) To find the straight-line distance to the airport:
1. Square the distance traveled north (100 km) and the distance traveled west (185 km).
Distance north squared = 100 km * 100 km = 10,000 km^2
Distance west squared = 185 km * 185 km = 34,225 km^2
2. Add the squared distances together.
10,000 km^2 + 34,225 km^2 = 44,225 km^2
3. Take the square root of the sum.
√(44,225 km^2) ≈ 210.32 km
Therefore, the straight-line distance to the airport is approximately 210.32 km.
B) To find the angle of elevation of the airplane from the point of view of the airport, you can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
1. The opposite side is the height of the airplane (7 km) and the adjacent side is the horizontal distance traveled west (185 km).
2. Use the formula tan(θ) = opposite/adjacent to find the angle of elevation (θ).
tan(θ) = 7 km / 185 km
3. Take the inverse tangent (arctan or tan^(-1)) of the ratio to find the angle.
θ = arctan(7 km / 185 km) ≈ 2.03°
Therefore, the angle of elevation of the airplane, from the point of view of the airport, is approximately 2.03°.