A 22-foot ladder leans against a house. The top of the ladder is 12 feet above the ground. Find the angle the ladder makes with the ground.
theta=arc sin 12/22
To find the angle that the ladder makes with the ground, we can use the properties of a right triangle. The ladder forms a right triangle with the ground and the side of the house.
We know the height of the ladder, which is 12 feet, and the length of the ladder, which is 22 feet. The angle we need to find is the angle opposite to the height of the ladder.
To find this angle, we can use the trigonometric function known as the inverse tangent (often written as atan). In this case, we can use the inverse tangent function to find the angle opposite the height.
The formula for finding this angle is:
angle = atan(height/length)
In this case, height = 12 feet and length = 22 feet, so we can substitute those values into the formula to calculate the angle.
angle = atan(12/22)
Using a calculator, the approximate value of the inverse tangent of 12/22 is 29.74 degrees.
Therefore, the angle that the ladder makes with the ground is approximately 29.74 degrees.