Question

A plane rises from take-off and

flies at an angle of 20° with
the horizontal runway. When it
has gained 750 feet, find the
distance that the plane has
flown.
+
A
C =
(Round the answer to the nearest whole number.)
c = ?
20°
B
M
B
750 ft
C
2
L

Answer 1

To find the distance that the plane has flown, we can use the concept of trigonometry. In the given scenario, we have a right triangle ABC, where AB represents the horizontal distance flown by the plane, BC represents the vertical distance gained (750 ft), and AC represents the total distance flown.

We are given that angle BAC is 20°, and BC is 750 ft. We need to find AC, the distance flown.

Using trigonometry, we can use the sine function to relate the angle and the sides of the triangle:

sin(angle) = opposite/hypotenuse

In this case, sin(20°) = BC/AC

Rearranging the equation, we have:

AC = BC / sin(angle)

Substituting the given values, we get:

AC = 750 ft / sin(20°)

Using a calculator, we can evaluate sin(20°) ≈ 0.3420

AC = 750 ft / 0.3420 ≈ 2192 ft

Therefore, the distance that the plane has flown is approximately 2192 feet.