a 10-foot ladder is placed against the side of a building as shown i figure i below.the bottom of the ladder is 8 feet from the base of the building .in the order to increase the reach of the ladder against the building ,it is moved 4 feet closer to the base the bulding shown in figure 2..
For figure one you have to find the missing side. You would have to use the Pythagorean theorem which is a^2 + b^2 = c^2. You should get 6. After that you have to use the same steps to find he missing part for figure 2. You should get 9.16. After you round you have to subtract the two from each other getting 3 or 3.2.
To calculate the new reach of the ladder against the building, we need to reevaluate the length of the hypotenuse formed by the ladder when it is moved closer to the base of the building.
In Figure 1, the ladder forms a right triangle with the base of the building and the ground. The length of the hypotenuse (the ladder) is given as 10 feet, and the distance between the base of the building and the ladder is 8 feet.
To calculate the height of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
Hypotenuse^2 = Base^2 + Height^2
Substituting the given values:
10^2 = 8^2 + Height^2
100 = 64 + Height^2
Height^2 = 100 - 64
Height^2 = 36
Height = √36
Height = 6 feet
So, the height of the building in Figure 1 is 6 feet.
Now, in Figure 2, the ladder is moved 4 feet closer to the base of the building. This means the distance between the base of the building and the ladder is reduced to 4 feet.
To calculate the new height of the building, we can use the same approach:
Hypotenuse^2 = Base^2 + Height^2
Substituting the new values:
10^2 = 4^2 + Height^2
100 = 16 + Height^2
Height^2 = 100 - 16
Height^2 = 84
Height = √84
Height ≈ 9.17 feet
Therefore, in Figure 2, the height of the building is approximately 9.17 feet. By moving the ladder 4 feet closer to the base, the reach against the building has increased by approximately 3.17 feet.