A 4.0 -m ladder leans against a vertical wall and makes an angle with the horizontal ground of 52degrees. What is the height above the ground where the ladder makes contact with the wall?
sin 52 degrees = x/4
Solve for x.
To find the height above the ground where the ladder makes contact with the wall, we can use trigonometric functions. In this case, we'll use the sine function.
Step 1: Identify the given values:
- The length of the ladder is 4.0 meters.
- The angle between the ladder and the horizontal ground is 52 degrees.
Step 2: Determine the trigonometric function to use:
Since we want to find the height above the ground, which is the opposite side to the angle, we'll use the sine function.
Step 3: Set up the equation:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height we're looking for, and the hypotenuse is the length of the ladder.
Step 4: Substitute the values into the equation:
sin(52 degrees) = height/4.0 meters
Step 5: Solve the equation:
To isolate the height, we can rearrange the equation:
height = sin(52 degrees) * 4.0 meters
Using a calculator, calculate sin(52 degrees), and then multiply it by 4.0 meters to find the height.
After performing the calculations, you'll find that the height above the ground where the ladder makes contact with the wall is approximately 3.02 meters.