Question

Paul is locked out of his house. An 18-ft ladder is outside and an upstairs window is open. Paul read the safety warning on the ladder recommending it be placed six feet away from the wall. He placed the ladder according to the warning and it reached the base of the window. How high is the base of the window off the ground?

Answer 1

Answer:

17.0 ft

Step-by-step explanation:

Let h be the height of the base of the window from the ground, L be the length of the ladder = 18 ft and d be the distance of the ladder from the wall = 6 ft. Now, these three lengths form a right-angled triangle with the length of the ladder, L as the hypotenuse side.

So, using Pythagoras' theorem,

L² = h² + d²

So, h = √(L² - d²)

Substituting the values of L = 18 ft and d = 6 ft, we have

h = √((18 ft)² - (6 ft)²)

= √(324 ft² - 36 ft²)

= √288 ft²

= 16.97 ft

≅ 17.0 ft