Question

1. identify structure how do you use the pythagorean theorem? write the pythagorean theorem. how do you find a when b and c are known? how do you find c when a and b are known?

Explanation:

Write the Pythagorean Theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\).

How do you find \(a\) when \(b\) and \(c\) are known?

Start with the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\).
Subtract \(b^{2}\) from both sides: \(a^{2}=c^{2}-b^{2}\).
Then take the square root of both sides: \(a = \sqrt{c^{2}-b^{2}}\) (we consider the non - negative root since \(a\) represents the length of a side of a triangle).

How do you find \(c\) when \(a\) and \(b\) are known?

Start with the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\).
Take the square root of both sides: \(c=\sqrt{a^{2}+b^{2}}\) (we consider the non - negative root since \(c\) represents the length of the hypotenuse of a triangle).

Answer:

• Pythagorean Theorem: \(a^{2}+b^{2}=c^{2}\)
• When finding \(a\) (\(b\) and \(c\) known): \(a = \sqrt{c^{2}-b^{2}}\)
• When finding \(c\) (\(a\) and \(b\) known): \(c=\sqrt{a^{2}+b^{2}}\)