Question

You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage. You are standing on a platform, which places your eyes at 6.5 feet. What is the distance from your eyes to the stage

Answer 1

The distance from your eyes to the stage is 8.85 ft

Explanation:

Your distance to the stage is 6 feet

Your eyes are 6.5 feet tall

You need to find the distance of your eyes towards the stage.

This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.

Observe the attached image.

Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.

So, using the Pythagorean theorem we have:

`z ^ 2 = h ^ 2 + x ^ 2\\\\z = √(h^2 +x^2)`

Where

`h = 6.5\ ft\\\\x = 6\ ft`

therefore:

`z = √((6.5)^2 +(6)^2)\\\\z =8.85\ ft`