A fence 5 feet tall runs parallel to a tall building at a distance of 2 feet from the building. We want to find the the length of the shortest ladder that will reach from the ground over the fence to the wall of the building.

Here are some hints for finding a solution:
Use the angle that the ladder makes with the ground to define the position of the ladder and draw a picture of the ladder leaning against the wall of the building and just touching the top of the fence.

If the ladder makes an angle 0.3 radians with the ground, touches the top of the fence and just reaches the wall,

1)calculate the distance along the ladder from the ground to the top of the fence?

2)The distance along the ladder from the top of the fence to the wall is?

Using these hints write a function L(x) which gives the total length of a ladder which touches the ground at an angle x, touches the top of the fence and just reaches the wall.
3)L(x) =?
Use this function to find the length of the shortest ladder which will clear the fence.
4)The length of the shortest ladder is feet?

To solve this problem, we can use trigonometry and geometry principles. Let's go step by step:

1) To calculate the distance along the ladder from the ground to the top of the fence, we can use the sine function. The height of the fence is 5 feet, and the angle the ladder makes with the ground is 0.3 radians. So, the distance along the ladder from the ground to the top of the fence can be found using the equation:

Distance = height of fence / sin(angle) = 5 / sin(0.3)

2) The distance along the ladder from the top of the fence to the wall can be calculated using the cosine function. We know that the ladder is 2 feet away from the building, and the angle it makes with the ground is still 0.3 radians. So, the distance along the ladder from the top of the fence to the wall can be found using the equation:

Distance = distance from fence to wall / cos(angle) = 2 / cos(0.3)

Now, we can write the function L(x) that gives the total length of a ladder which touches the ground at an angle x, touches the top of the fence, and just reaches the wall:

L(x) = Distance from ground to fence + Distance from fence to wall
= 5 / sin(x) + 2 / cos(x)

3) Using the function L(x), we can find the length of the shortest ladder that will clear the fence. We want to minimize the length of the ladder, so we need to find the minimum value of L(x).

The minimum value of L(x) can be found by taking the derivative of L(x) with respect to x, setting it equal to zero, and solving for x. Once we have the value of x, we can substitute it back into L(x) to find the minimum length.

4) The length of the shortest ladder is the value of L(x) when x is the angle that gives the minimum value. In other words, the length of the shortest ladder is L(x_min).

To find the exact length of the shortest ladder, we need to use the specific values of x_min and substitute them into the equation L(x).

Note: Since we don't have the value of x_min, we cannot calculate the exact length of the shortest ladder at this point. You would need to find the value of x that minimizes L(x) to determine the shortest ladder length.

A 27 ft ladder leans against a building so that the angle between the ground and the ladder is 75 degrees