Proof for Euler's Theorem

I'd like a proof for Euler's theorem that can be understood by a high school student.

Total area of a triangle

A 1 acre field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each of the side of the post on the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is the total area the two sheep have to themselves?

A 1 acre area field in the shape of a right triangle has a post at the midpoint of each side

A 1 acre area field in the shape of a right triangle has a post at the midpoint of each side. A sheep is tethered to each side posts and a goat to the post in the hypotenuse. The ropes are just long enough to let each animal reach the two adjacent vertices. What is thw total area the two sheep have to themselves? i.e. the area t ...continues

determining the distance

Joe and jill set sail from the same point, with Joe sailing in the direction of S4degree east and Jill sailing in the direction S9degree west. After 4 hr, Jill 2 mi due west of Joe. How far had jill sailed?

Understanding solid figures.

What are solid figures?

industrial application help

The two images below shows one of our attempts to come up with the rotation angle required. I believe that it does not work because we are using first order trig which assumes symmetry . Please comment on this assumption and or why it does not work. See attachment

Working with area and perimeter of a triangle

In triangle ABC, the lengths of line AB and line BC equal 13 centimeters. If the perimeter of triangle ABC is 36 centimeters, what is the area in square centimeters of triangle ABC?

Proofs!

I am trying to figure out how to prove opposite angles of a quadrilateral are supplementary.The quadrilateral is inscribed in the circle

Rigid Pentagonal Prism

How many lines would you need to add to a pentagonal prism anchored to the ground to make it rigid?

How to factor polynomials

Factor the polynomial: x2+4x-4=0