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

Accepted Solution

Answer: The distance from your eyes to the stage is 8.85 ftStep-by-step explanation:Your distance to the stage is 6 feetYour eyes are 6.5 feet tallYou 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:[tex]z ^ 2 = h ^ 2 + x ^ 2\\\\z = \sqrt{h^2 +x^2}[/tex]Where[tex]h = 6.5\ ft\\\\x = 6\ ft[/tex]therefore:[tex]z = \sqrt{(6.5)^2 +(6)^2}\\\\z =8.85\ ft[/tex]