A 20 foot extension ladder leans against Paul’s barn wall creating a 65° angle with the ground. How many feet (to the nearest tenth) above the ground is the point where the ladder touches the wall?
x/20 = sin 65°
the height is the side opposite the 65° angle.
sine is opposite/hypotenuse
I need a little more explanation please maybe step by step and the answer
To find the height above the ground where the ladder touches the wall, we can use trigonometry. Specifically, we will use the sine function since we have the angle and the length of the ladder.
Step 1: Draw a right triangle. Label one of the legs as the height (h), with the opposite angle to that leg labeled as 65°. Let the hypotenuse represent the ladder, so label it as 20 feet.
Step 2: Recall that sine (sin) is defined as the ratio of the length of the side opposite the angle to the hypotenuse. In this case, sin(65°) = h / 20.
Step 3: Rearrange the equation to solve for h: h = 20 * sin(65°).
Step 4: Calculate h using a scientific calculator or an online trigonometry calculator. The result is approximately 18.1 feet.
Therefore, the point where the ladder touches the wall is about 18.1 feet above the ground.