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

Answer:

The distance from your eyes to the stage is 8.85 ft

Step-by-step 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:

$z ^ 2 = h ^ 2 + x ^ 2\\\\z = \sqrt{h^2 +x^2}$

Where

$h = 6.5\ ft\\\\x = 6\ ft$

therefore:

$z = \sqrt{(6.5)^2 +(6)^2}\\\\z =8.85\ ft$