Question

A ladder is leaning against the side of a house and forms a 65° angle with the ground. The foot of the ladder is 8 feet from the house. Find the length of the ladder to the nearest tenth of a foot.

8.8 ft
3.7 ft
18.9 ft
17.2 ft

Answer 1

Answer: 18.9 ft

Explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.

cos α = adjacent side / hypotenuse

Where α is the angle of elevation of the ladder to the ground, the hypotenuse (x) is the longest side of the triangle (in this case is the length of the ladder), and the adjacent side (x) is the distance between the foot of the ladder and the house.

Replacing with the values given:

cos 65= 8 /x

Solving for x:

x= 8/cos65

x = 18.9 feet

Feel free to ask for more if needed or if you did not understand something.