Question

Ella is stuck at the top of the Ferris wheel her mother is standing 26 feet from the base of the wheel looking better if the angle of elevation from Mom to LA is 68° what is the diagonal distance between Ella and her mom

Answer 1

Using trigonometry, the diagonal distance between Ella and her mom is approximately 64.1 feet.

How the diagonal distance is determined:

The position of Ella = the top of the Ferris wheel

The position of Ella's mother = standing 26 feet from the base of the wheel

The angle of elevation from Ella’s mother to Ella = 68°

Let’s assume that the height of the Ferris wheel is h feet and the diagonal distance between Ella and her mom is d feet.

Then, using the tangent function, we can find h:

tan(68⁰) = 26h​

Solving for h:

h = 26tan(68⁰) ≈ 63.6 feet

Using the Pythagorean theorem to find d:

`d^2 =h^2+26^2`

Solving for d:

`d = √(h^2+26^2)` ​≈ 64.1 feet

Thus, the diagonal distance between Ella and her mom is approximately 64.1 feet.