Question

A right triangle has a hypotenuse length of 13 units. One leg has a length of 12 units. Which equation can be used to determine the length of the other leg?
LaTeX: a^2=12^2+13^2 a 2 = 12 2 + 13 2

LaTeX: a=\sqrt{13^2-12^2} a = 13 2 − 12 2

LaTeX: a^2=12^2-13^2 a 2 = 12 2 − 13 2

LaTeX: a=\sqrt{12^2+13^2}

Answer 1

a = √(13² - 12²) units

Further explanation

Given:

• A right triangle has a hypotenuse length of 13 units.
• One leg has a length of 12 units

Question:

Which equation can be used to determine the length of the other leg?

The Process:

We will solve a problem regarding right triangles. In the process, there is a relationship between the Pythagorean Theorem with Exponent and Square Root.

Let us find out the equation to determine the length of the other leg. Let the length of the leg as "a".

The Phytagorean Theorem:

$\boxed{ \ (leg)^2 + (leg)^2 = (hypotenuse)^2 \ }$

$\boxed{ \ a^2 + 12^2 = 13^2 \ }$

Subtract by 12² on both sides.

$\boxed{ \ a^2 = 13^2 - 12^2 \ }$

To take the square root on both sides.

So here's the equation that can be used to determine the length of the other leg: $\boxed{\boxed{ \ a = \sqrt{13^2 - 12^2} \ }}$

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Notes

If we continue working on the above, the results will be as follows:

$\boxed{ \ a = \sqrt{13^2 - 12^2} \ }$

$\boxed{ \ a = \sqrt{169 - 144} \ }$

$\boxed{ \ a = \sqrt{25} \ }$

Hence the length of the other leg equal to a = 5 cm.

Of course, we agree with the use of the right intuition, which is to remember Pythagorean Triples, i.e., $\boxed{ \ 5-12-13 \ }.$ This method is very convenient when working on multiple-choice tests in a limited amount of time.

Learn more

1. What are the lengths of the legs of the triangle? brainly.com/question/13027296
2. Find out the measures of the two angles in a right triangle brainly.com/question/4302397
3. A word problem of a quadratic equation brainly.com/question/11805547