The 8-ft wall shown here stands 27 ft from the building. Find the lenght of the shortest straight beam that will reach to tthe side of the building from the ground outside the wall.

ANSWER 46.87ft
How do i solve???

To solve this problem, we can use the Pythagorean Theorem. The theorem states that in a right-angled 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, the wall, the beam, and the ground outside the wall form a right-angled triangle.

Let's assume the length of the beam is x. We can set up the following equation using the Pythagorean Theorem:

x^2 = 8^2 + 27^2

Simplifying the equation, we get:

x^2 = 64 + 729
x^2 = 793

Taking the square root of both sides to solve for x, we get:

x = √793

Calculating the value, we find that x is approximately equal to 28.12 ft.

However, this is the length of the hypotenuse of the triangle. We need to find the length of the shortest straight beam, which will be the height of the triangle. To find the height, we subtract the height of the wall (8 ft) from the length of the hypotenuse:

Height = x - 8
Height = 28.12 ft - 8 ft
Height = 20.12 ft

Therefore, the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall is approximately 20.12 ft.

To solve this problem, you can use the Pythagorean Theorem, which 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 lengths of the other two sides.

Here's how you can solve the problem step by step:

1. Draw a diagram of the situation described. Label the length of the wall as 8 ft and the distance from the wall to the building as 27 ft.

_____
| |
|Wall |
| |
______|_____|______
| |
| Building |
| |
|_________________|
27 ft

2. Denote the length of the shortest straight beam as 'x' (the hypotenuse of the right triangle formed by the wall, the ground, and the beam).

x
_____
| |
|Wall |
| |
|_____|
27 ft

3. Use the Pythagorean Theorem to set up an equation:

x^2 = 8^2 + 27^2

4. Simplify the equation:

x^2 = 64 + 729

5. Add the numbers on the right side of the equation:

x^2 = 793

6. Take the square root of both sides of the equation to solve for 'x':

x = √793 ≈ 28.15 ft

So, the length of the shortest straight beam that will reach to the side of the building from the ground outside the wall is approximately 28.15 ft.

Use similar triangles. Let x be the length from the wall to the point the board touches the ground.

Length/(27+x)= sqrt(64+x^2)/x
from similar triangles.

Length= (27+x)/x * sqrt(64+x^2)

Now, find dL/dx and set to zero. Solve for x. Watch your algebra.

No, it's 9001