Show using the law of cosine that if (Y)= 90degrees then c^2=a^2+b^2?

Question

the Y in cosine is the greek symbol Gamma

Answer 1

The simplest way to show this is that if you have a 90 degree angle in the triangle, then you have a right triangle. You can then use the pythagorean theorem to solve. The Pythagorean theorem states that for a right triangle with legs a and b and the hypotenuse c (opposite the right angle) then

a^2 + b^2 = c^2

You can also use Law of Cosines

c^2 = a^2 + b^2 - 2abCos C

the Cos of a 90 degree angle is 0; this gives the following on the right hand side
a^2 + b^2 - 2ab * 0
or just a^2 + b^2

Hope this helps
Good Luck

Answer 2

The law of cosines says that c² = a² + b² -2ab cos γ,
where γ is the angle opposite side c.
If γ = 90 degrees, then cos γ = 0, so c² = a² + b².