Question

mr. singh has two ladders, one is 9 feet tall and the other is 12 feet tall. he needs to reach a window that is 10 feet off the ground. he must place the ladder 4 feet from the house due to a shrub being in the way. which ladder should mr. singh use to reach the window? the distance from the base of the ladder to the window is \boxed{} feet. mr. singh should use the \boxed{}-foot ladder in order to reach the window.

Explanation:

Step1: Identify right triangle sides

We have a right triangle where one leg is the height of the window ($a = 10$ ft), the other leg is the distance from the house ($b = 4$ ft), and the ladder is the hypotenuse ($c$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c = \sqrt{a^2 + b^2}$. Substitute the values:
$$c = \sqrt{10^2 + 4^2} = \sqrt{100 + 16} = \sqrt{116} \approx 10.77 \text{ ft}$$

Step3: Compare to ladder lengths

The 9-foot ladder is shorter than 10.77 ft, so it cannot reach. The 12-foot ladder is longer than 10.77 ft, so it can reach.

Answer:

The distance from the base of the ladder to the window is $\sqrt{116} \approx 10.77$ feet.
Mr. Singh should use the 12-foot ladder in order to reach the window.