Assuming the ground and wall meet at a 90 degree angle, we can set up a right triangle with 20 feet as the hypotenuse and 65 degrees as the angle between the hypotenuse and adjacent side. The number of feet in which the ladder reaches up the wall would be the side opposite of the angle.
To solve for the opposite side, we can use the trigonometric function sine:
[tex]sin(\theta)= \frac{opposite}{hypotenuse} [/tex]
Plug in what we know:
[tex]sin(65) = \frac{y}{20} [/tex]
Solve for y:
y = [tex]20sin(65) = 18.126[/tex]
The answer to the nearest tenth is 18.1 feet.
