Question

Firefighter is attempting to rescue James at the top of a burning 5-story building. The ladder can extend between 50 feet and 120 feet. The ladder was placed against the building which casted a shadow at the base of the building with an angle of elevation of 45∘

45

∘
. Which one of the following represents the length of the ladder used to rescue James? (1 story = 10 feet)

Answer 1

Answer: 70.71 feet

Step-by-step explanation: Work attached in the image. It's helpful to draw a picture for these type of problems. In this case, we are solving for the hypotenuse of a triangle, which is the length of the ladder. Since we know an angle and a side, we can use a trigonometric function to solve for the hypotenuse. The angle is 45 and the side we are given is opposite of the angle, which is 50 feet. So, we can use sin45 = 50/x and solve for x, which is the length of the ladder. The length of the ladder is 70.71 feet.