You have a 20-foot ladder that you are using as you paint your house. You place the ladder so that it forms an angle of 30 at the point of contact between the ladder and the ground. How high will the top of the ladder be above the ground?

Please explain. thank you

10 sin φ=h/L

h=Lsin 30=L/2

To find how high the top of the ladder will be above the ground, we can use trigonometric functions. In this case, we can use the sine function.

Step 1: Identify the given information:
- The length of the ladder is 20 feet.
- The angle formed between the ladder and the ground is 30 degrees.

Step 2: Select the appropriate trigonometric function:
Since we are looking for the height (opposite side) and we know the angle and the length of the ladder (hypotenuse), we'll use the sine function.

Sine function: sin(angle) = opposite/hypotenuse

Step 3: Substitute the given values into the equation:
sin(30) = opposite/20

Step 4: Solve for the opposite side (height):
opposite = sin(30) * 20

Step 5: Calculate the value:
opposite = 0.5 * 20 = 10 feet

Therefore, the top of the ladder will be 10 feet above the ground.