Question

Sauron is looking down at the hobbits from The Dark Tower at a 28º angle. His tower stands 1,400 meters tall. How far are Frodo and Sam from The Dark Tower?

Answer 1

By using what we know about right triangles, we will see that the hobbits are at 744.39 meters from the Dark Tower.

How far are the hobbits from the Dark Tower?

We can think of this situation as in a right triangle, where the catheti are the height of the tower and the distance between the hobbits and the Dark Tower.

Then we can use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

Where θ = 28°

The adjacent cathetus to this angle is the height of the tower, then:

Adjacent cathetus = 1,400 m

And the opposite cathetus is the distance that we want to find, let's call it D.

Tan(28°) = D/1,400m

Solving for D we get:

Tan(28°)*1,400m = D = 744.39m

The hobbits are at 744.39 meters from the Dark Tower.

If you want to learn more about right triangles, you can read:

brainly.com/question/2217700