An 18 foot ladder is leaned against a wall .if the base of the ladder is 8 feet from the wall,how high up on the wall will the ladder reach?
Ajay leans a 18-foot ladder against a wall so that it forms an angle of 73^{\circ}
∘
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
To determine the height the ladder will reach on the wall, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) 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 distance from the base of the ladder to the wall forms one of the other sides. Let's call this distance "x" (the height up on the wall the ladder will reach).
Using the Pythagorean theorem, we can write the equation as follows:
8^2 + x^2 = 18^2
Simplifying the equation:
64 + x^2 = 324
Now, we'll isolate x by subtracting 64 from both sides of the equation:
x^2 = 324 - 64
x^2 = 260
To find the value of x, we take the square root of both sides:
√x^2 = √260
x ≈ √260
The approximate value of the square root of 260 is 16.12.
Therefore, the ladder will reach approximately 16.12 feet up on the wall.
16.1
The ladder is the hypotenuse of a right-angle triangle.
Use the Pythagorean Theorem.