If a right triangle has legs measuring 10 cm and 24 cm, how long is the hypotenuse? (1 point)
The length of the hypotenuse can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, the lengths of the legs are given as 10 cm and 24 cm. Let's assume the length of the hypotenuse is "c".
The Pythagorean theorem equation is:
c^2 = a^2 + b^2
Substituting the values given:
c^2 = 10^2 + 24^2
c^2 = 100 + 576
c^2 = 676
Taking the square root of both sides:
c = √676
c ≈ 26.00 cm
Therefore, the length of the hypotenuse is approximately 26.00 cm.
Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window? (1 point)
To find the distance Camila should set up the ladder from the base of the house, we can use the Pythagorean theorem.
Let "x" be the distance from the base of the house to where Camila sets up the ladder. The height of the ladder will be the same as the height of the window, which is given as 16 ft.
The length of the ladder, the hypotenuse, is given as 20 ft.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
20^2 = x^2 + 16^2
400 = x^2 + 256
Subtracting 256 from both sides:
400 - 256 = x^2
144 = x^2
Taking the square root of both sides:
12 = x
Therefore, Camila should set up the ladder 12 ft from the base of the house, so that the top of the ladder is exactly at the bottom of the window.