MarkFL said:According to Pythagoras, we should have:
\(\displaystyle u^2+v^2=w^2\)
Plug in the given values:
\(\displaystyle \left(\frac{2(m+n)}{n}\right)^2+\left(\frac{4m}{m-n}\right)^2=\left(\frac{2(m^2+n^2)}{(m-n)n}\right)^2\)
I would multiply through by \(\displaystyle (n(m-n))^2\) to get:
\(\displaystyle (2(m+n)(m-n))^2+(4mn)^2=(2(m^2+n^2))^2\)
\(\displaystyle (2(m^2-n^2))^2+(4mn)^2=(2(m^2+n^2))^2\)
Continuing, you will obtain an identity. :D
A right triangle is a type of triangle that has one angle measuring 90 degrees. This angle is often referred to as the "right angle".
A right triangle has three sides: the hypotenuse, which is the longest side and is opposite the right angle, and the two shorter sides, known as the legs, which form the right angle.
The Pythagorean theorem can be used to calculate the missing sides of a right triangle. It states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The three main trigonometric ratios used in right triangles are sine, cosine, and tangent. These ratios represent the relationship between the sides of a right triangle and its angles.
Right triangles are commonly used in fields such as engineering, architecture, and physics to calculate distances, angles, and forces. They are also used in navigation, surveying, and map making.