A ladder is placed 4 ft from the side of a building. The top of the ladder must be 13 ft off the ground. What is the shortest ladder that will do the job?
4^2 + 13^2 = x^2
16+169=185^
=34,225
16 + 169 = 185 = x^2
so
x = square root of 185 = 185^0.5
= 13.6
To find the length of the ladder, we can use the Pythagorean theorem. The theorem states that for 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 forms the hypotenuse of a right triangle, with one side being the height of the building and the other side being the distance of the ladder from the building.
Let's use the variables a, b, and c to represent the sides of the triangle. The side of the building, which is 13 ft, will be the height, so a = 13. The distance of the ladder from the building, which is 4 ft, will be the base, so b = 4. The length of the ladder, which is what we want to find, will be the hypotenuse, so c = x.
Now we can use the Pythagorean theorem: a^2 + b^2 = c^2
Plugging in the values, we get:
13^2 + 4^2 = x^2
169 + 16 = x^2
185 = x^2
To solve for x, we take the square root of both sides:
sqrt(185) = sqrt(x^2)
x = sqrt(185)
So the length of the ladder is sqrt(185), which is approximately equal to 13.60 ft.