In a right triangle ABC, where ∠B is the right angle, AB=5 units, and BC=12 units. Find the length of the hypotenuse AC.

Question

We can use the Pythagorean theorem to find the length of the hypotenuse AC.

Answer 1

[Tutor's NOTE: Whatever is inside the brackets is my Tutor's notes, so the solution suggested to a student, is what is outside of the brackets; use it on the test.]

[Observe the Given, use shortcuts. Especially important on a timed test like Digital SAT. Also, it's a way to avoid errors.]

[A Pythagorean triad (or triple) is a set of three positive integers (a, b, c) that perfectly satisfy the Pythagorean theorem: a² + b² = c². This is what is taught in school, and is immediately available.]

5, 12, and 13 is a Pythagorean triad.

Answer: |AC| = 13

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[If Pythagorean triads forgotten, use the Pythagorean Theorem:]

Pythagorean Theorem: |AC|² = |AB|² + |BC|²

_{__________________ ___________ ____}

|AC| = √|AB|² + |BC|² = √5² + 12² = √169 = 13

Answer: |AC| = 13

Answer 2

Practice question on the pythagorean theorem!

Answer 3

What we call the pythagorean theorem states that the square of one leg's length plus the square of the other leg's length gives the square of the length of the hypotenuse.

In symbols, this is the equation a² + b² = c²

The segment from A to B is one leg and its length is 5 units. 5² = 25.

The segment from B to C is the other leg and its length is 12 units. 12² =144.

Plugging into the formula we get

5² + 12² = (AC)²

169 = (AC)².

Now we have to take the square root of both sides.

√ (169) = √(AC)²

13 = AC

The length of the hypotenuse is 13 units.

A triangle with side lengths of 5,12 & 13 is one you should keep in mind going forward.

It will always be a right triangle.

Answer 4

AC² = 5² + 12², by the Pythagorean Theorem