A ladder is leaning up against a wall. The ladder touched the wall 5ft up. The ladder is 6ft Long.

A) Draw a picture and label all of the values

B) What is the angle that is made between the ladder and the ground?

C) How far away from the wall is the ladder where it touches the ground?

b. what is arcsin(5/6)?

c. distance=sqrt(36-25)

A) To draw a picture and label all of the values, we can start by drawing a vertical line to represent the wall. Then, draw a slanted line starting from the bottom of the vertical line, which represents the ladder leaning against the wall. Label the point where the ladder touches the wall as "A" and write 5ft next to it. Label the bottom of the ladder (where it touches the ground) as "B" and write the length of the ladder, which is 6ft, next to it.

B) To find the angle made between the ladder and the ground, we can use trigonometry. Specifically, we can use the sine function. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse (in this case, the ladder). Let's call the angle between the ground and the ladder "θ".

Using the given information, we have the opposite side as 5ft (the height of the ladder touching the wall) and the hypotenuse as 6ft (the length of the ladder). Therefore, we can write the equation sin(θ) = 5/6.

To find the angle θ itself, we can use the inverse sine function (also known as arcsine). Taking the inverse sine of both sides, we get θ = sin^(-1)(5/6). Using a calculator, we can find the approximate value of θ.

C) To determine how far away from the wall the ladder touches the ground, we can use the cosine function. The cosine of an angle is equal to the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

In this case, the adjacent side is what we want to find (the distance from the wall where the ladder touches the ground), and the hypotenuse is the length of the ladder (6ft). Let's call the distance from the wall where the ladder touches the ground "x".

Using the given information, we have the adjacent side as x and the hypotenuse as 6ft. Therefore, we can write the equation cos(θ) = x/6.

To find the value of x, we need to rearrange the equation. Multiply both sides by 6 to get 6cos(θ) = x.

Now, we can substitute the value of θ that we found in part B to get 6cos(sin^(-1)(5/6)) = x. Using a calculator, we can find the approximate value of x.