2. A 10 foot ladder is leaning against a house. The bottom of the ladder is 5 feet from the building. How high is the top of the ladder? Round to the nearest hundredth.
Use Pythagorean theorem.
a^2 + b^2 = hypotenuse^2
5^2 + b^2 = 10^2
Solve for b.
a lader that is 10 ft long leans against a building.the bottom of the ladder is 6 ft away from the base of the building .how far up dies the ladder reach?
To solve this problem, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder, the house, and the ground form a right triangle. The distance from the bottom of the ladder to the building is one of the sides, and the height of the ladder (the distance from the ground to the top of the ladder) is the other side. The ladder itself is the hypotenuse.
We know that the bottom of the ladder is 5 feet from the building, and the ladder is 10 feet long. Let's call the height of the ladder h.
Using the Pythagorean theorem, we can write the equation:
5^2 + h^2 = 10^2
25 + h^2 = 100
To solve for h, we subtract 25 from both sides:
h^2 = 100 - 25
h^2 = 75
Taking the square root of both sides, we get:
h = √75
Now, we can approximate the value of h to the nearest hundredth:
h ≈ 8.66 feet
So, the top of the ladder is approximately 8.66 feet high.