A 104 ft. ladder is leaned against a wall. If the base of the ladder is 40 ft. from the wall, how high up the wall will the ladder reach?
104ft.^2 + b^2 = 40ft.^2
10,816 + b^2 = 1,600
0 + b^2 = 10,816 - 1,600 = 9,216
C^2 = SQRT of 9,216 or 96ft.
Wow, a 100 ft ladder ????
And the base is 40 ft out ???
totally totally unsafe , absurd and against all safety regulations.
Yes, your answer is right.
To calculate the height the ladder will reach on the wall, we can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the base of the ladder and the height on the wall).
In this case, we have:
104ft^2 = 40ft^2 + h^2
10400 sq. ft. = 1600 sq. ft. + h^2
Now, let's subtract 1600 sq. ft. from both sides:
10400 sq. ft. - 1600 sq. ft. = h^2
8840 sq. ft. = h^2
To find the height h, we can take the square root of both sides:
sqrt(8840 sq. ft.) = sqrt(h^2)
93.97 ft. = h
Therefore, the ladder will reach a height of approximately 93.97 ft. on the wall.
To find out how high up the wall the ladder will reach, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides (in this case, the height and the base of the ladder).
Let's represent the height of the wall as 'b' and the length of the ladder as 104ft. The base of the ladder is given as 40ft. According to the Pythagorean theorem, we have the equation:
104ft^2 = 40ft^2 + b^2
To solve for 'b', we first need to subtract 40ft^2 from both sides:
104ft^2 - 40ft^2 = b^2
Simplifying this equation, we get:
10,816 = b^2
Next, take the square root of both sides to solve for 'b':
√10,816 = √(b^2)
This gives us:
b = √10,816
Now we need to calculate the square root of 10,816, which is approximately 104ft.
Therefore, the ladder will reach a height of approximately 104ft up the wall.