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:
[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]
