Answer:
<em> The distance from your eyes to the stage is 8.85 ft</em>
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.
<u>Observe the attached image.</u>
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}](https://tex.z-dn.net/?f=z%20%5E%202%20%3D%20h%20%5E%202%20%2B%20x%20%5E%202%5C%5C%5C%5Cz%20%3D%20%5Csqrt%7Bh%5E2%20%2Bx%5E2%7D)
Where
![h = 6.5\ ft\\\\x = 6\ ft](https://tex.z-dn.net/?f=h%20%3D%206.5%5C%20ft%5C%5C%5C%5Cx%20%3D%206%5C%20ft)
therefore:
![z = \sqrt{(6.5)^2 +(6)^2}\\\\z =8.85\ ft](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B%286.5%29%5E2%20%2B%286%29%5E2%7D%5C%5C%5C%5Cz%20%3D8.85%5C%20ft)