We know that a radio tower has supporting cables attached to it at points 100 feet above the ground.
We want to write a model for the length d of each supporting cable as a function of the angle θ that it makes with the ground. As we can see, the tower and the cables form a right triangle with the ground.
Since we know the length of the height, we can use the trigonometric ratio for sine to find the expression for d.
sin θ = Opposite/Hypotenuse
In this case, the length of the opposite side is 100 and the length of the hypotenuse is d.
sin θ = Opposite/Hypotenuse ⇒ sin θ = 100/d
Let's solve this equation to obtain an expression for d.
