a ladder 38 feet long is leaning against the side of a wall. if the angle between the ladder and the wall is 54 (degrees) approximately how far is the bottom of the ladder from the wall?

x/38 = sin 54°

30.74264579

To find out how far the bottom of the ladder is from the wall, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground. The angle between the ladder and the wall is given as 54 degrees.

Since the ladder is the hypotenuse of the right triangle, we can use the sine function to determine the length of the side opposite the angle (which represents the distance between the bottom of the ladder and the wall).

The formula for sine is:

sin(angle) = opposite/hypotenuse

In this case, the angle is 54 degrees, and the hypotenuse (ladder) is 38 feet. We want to find the opposite side, which represents the distance between the bottom of the ladder and the wall.

Rearranging the formula to solve for the opposite side:

opposite = sin(angle) * hypotenuse

Plugging in the values:

opposite = sin(54) * 38

Using a calculator, we find that sin(54) is approximately 0.809.

opposite ≈ 0.809 * 38

opposite ≈ 30.802

Therefore, the bottom of the ladder is approximately 30.802 feet away from the wall.