To solve this problem, we will use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's represent the height of the ladder as h and the distance from the base of the ladder to the house as d. We can set up the following equation:
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we have:
h ≈ √108
h ≈ 10.4
Therefore, the ladder will reach approximately 10.4 ft high, so the answer is c. 10.4 ft.
Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?
a. 108 ft.
b. 13.4 ft.
c. 10.4 ft.
d. 180 ft.
1 answer