3. Suppose a ladder is 12 ft. long. The base of the ladder is 5 ft. from a wall, and the top of the ladder is leaning against the wall. How far above the ground is the tip of the ladder?
Use the Pythagorean Theorem -- with c = 12 and b = 5. Solve for a.
a^2 + b^2 = c^2
use a^2 +b^2=c^2
144+25=c^2
169= c^2
13=c so 13ft.
To find the height of the wall that the ladder is leaning against, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 other two sides.
In this case, the ladder forms the hypotenuse of the right triangle, and the base of the ladder (5 ft) is one of the sides. Let's call the height of the wall h ft.
Using the Pythagorean theorem, we have:
(12 ft)^2 = (5 ft)^2 + h^2
Simplifying this equation, we get:
144 ft^2 = 25 ft^2 + h^2
Subtracting 25 ft^2 from both sides:
119 ft^2 = h^2
Taking the square root of both sides:
sqrt(119 ft^2) = sqrt(h^2)
√119 ft = h
Therefore, the tip of the ladder is approximately √119 ft or about 10.92 ft above the ground.