Question

If the hypotenuse of a 45°-45°-90° triangle has a length of √2, how long are the legs?

Right triangles and trigonometry
ANSWERED
asked 2021-06-15

If the hypotenuse of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle has a length of \(\displaystyle\sqrt{2}\), how long are the legs?

Expert Answers (1)

2021-06-16

A \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle is a right isosceles triangle. If x is the length of each leg, we can use the Pythagorean Theorem to write: \(\displaystyle{x}^{{2}}+{x}^{{2}}={\left(\sqrt{2}\right)}^{{2}}\)
\(\displaystyle{2}{x}^{{2}}={2}\)
\(\displaystyle{x}^{{2}}={1}\)
\(x=1\)

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