Question

a 12 foot ladder leans against the side of a house the bottom of the ladder is 7 ft from the side of the house how high is the top of the ladder from the ground​

Answer 1

Using the Pythagorean theorem, the top of the ladder is found to be approximately 9.75 feet above the ground when the bottom is 7 feet away from the house.

Step-by-step explanation:

To find out how high the top of the ladder is from the ground, we can use the Pythagorean theorem. This theorem states that in a right-angled 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 lengths of the other two sides (the legs). If we let x represents the height from the ground to the top of the ladder, we can write an equation based on the given dimensions:

x2 + 72 = 122

Solving this equation for x gives us:

x2 = 122 - 72

x2 = 144 - 49

x2 = 95

x = √95 ≈ 9.7468 feet

So, the top of the ladder is approximately 9.75 feet above the ground.

Answer 2

he Pythagorean theorem states that, in a right triangle, the length of the hypotenuse squared equals the sum of the squares of the other two sides or legs of the triangle. Algebraically, a2+b2=c2. In your example, the length of the ladder would be the hypotenuse and the distance from the wall would be one of the legs. So substitute these values into the equation to get: 32+b2=122 or 9+b2=144 and then subtract 9 from both sides to get b2=135. Therefore b=√135≈11.62. If your problem requires an exact answer in its most simplified form, please note that √135=3√15. Hope this helps you out.

Step-by-step explanation: