An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 40° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 50°, then how long is the slide?
A) 19 feet
B) 22 feet
C) 6 feet
D) no solution

Question

Quizplus · Accepted Answer

The slide forms the hypotenuse of a right triangle with the height of the door as one leg and the distance from the bottom of the door to where the slide touches the ground as the other leg. The angle formed by the hypotenuse and the leg representing the height of the door is 40°, and the angle formed by the hypotenuse and the leg representing the distance from the bottom of the door to where the slide touches the ground is 50°. Therefore, the angle formed by the two legs is 90°. Using the sine ratio, we can find the length of the slide:sin(40°) = height of door / length of slidesin(40°) = 5 feet / length of slidelength of slide = 5 feet / sin(40°)length of slide ≈ 7.66 feetTherefore, the length of the slide is approximately 7.66 feet, which is closest to choice A, 19 feet.

An Airplane Door Is 5 Feet High