Consider the right triangle shown, in which the two sides...

Consider the right triangle shown, in which the two sides have length $1 .$
(a) Using the Pythagorean Theorem, what is the length of the hypotenuse?
(b) Using the fact that the sum of the angles in a triangle is $180^{\circ}$ , what are the measures of the three angles?

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Key Concepts

Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry stating that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem provides a method to calculate the length of the hypotenuse when the lengths of the other two sides are known.

Isosceles Right Triangle

An isosceles right triangle is a right-angled triangle where the two legs are congruent. This equality leads to both legs having the same length, which in turn forces the two non-right angles to be equal. This property is crucial when calculating angle measures in such triangles.

Triangle Angle Sum

The Triangle Angle Sum concept refers to the principle that the interior angles of any triangle always add up to 180 degrees. This fact is used to determine unknown angles in a triangle, especially when one or more angles are already known or deduced from other properties.

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