We are given that Jason is adding a climbing wall to his little brother's swing-set, and we know that he starts building 5 feet out from the existing structure and that he wants it to have an angle of 60^(∘). Let's sketch a diagram describing the given situation.
Since we are asked to determine the length of the wall, let l represent this length.
Now let's recall the 30^(∘)-60^(∘)-90^(∘) Triangle Theorem. This theorem tells us that the length of the hypotenuse of this right triangle is 2 times the length of the shorter leg s and that the length of the longer leg is sqrt(3) times the length of the shorter leg.
According to this theorem, the value of l is two times the distance between Jason and the existing structure, 5.
l=2( 5)=10
The length of the wall is 10 feet.
