In a right triangle, one leg measures centimeters and the hypotenuse measures centimeters. What is the length, in centimeters, of the triangle's other leg?

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SAT Right Triangles & Trigonometry Question 13 | Free SAT Prep | Aniko

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Question 13·Easy·Right Triangles and Trigonometry

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In a right triangle, one leg measures $6$ centimeters and the hypotenuse measures $10$ centimeters. What is the length, in centimeters, of the triangle's other leg?

For right-triangle questions where two sides are given and one is missing, immediately write the Pythagorean theorem $a^2 + b^2 = c^2$ with the hypotenuse as $c$ . Substitute the known values, solve algebraically for the unknown squared, and then take the positive square root because side lengths are positive. Be careful not to mix up which side is the hypotenuse and not to stop at $x^2$ —always take the square root as the final step.

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Identify the key right-triangle relationship

You are given a right triangle with one leg and the hypotenuse. What formula connects the lengths of the two legs and the hypotenuse in a right triangle?

Set up an equation for the missing leg

Let the unknown leg be $x$ . Using the right-triangle formula, how can you write an equation involving $x$ , 6, and 10?

Solve carefully and remember the last step

After you get an equation like $x^2 = \text{(some number)}$ , what operation do you need to perform to solve for $x$ , and what should you remember about the sign of a side length?

Desmos Guide

Compute the missing leg length

In Desmos, type sqrt(10^2 - 6^2) and look at the numerical value that Desmos outputs; that value is the length of the other leg.

Step-by-step Explanation

Use the Pythagorean theorem

In a right triangle with legs $a$ and $b$ and hypotenuse $c$ , the Pythagorean theorem says

a^2 + b^2 = c^2.

Here, one leg is $6$ centimeters and the hypotenuse is $10$ centimeters, so let the unknown leg be $x$ and write

6^2 + x^2 = 10^2.

Solve for the square of the unknown leg

Compute the squares and isolate $x^2$ :

\begin{aligned} 6^2 + x^2 &= 10^2 \\ 36 + x^2 &= 100 \end{aligned}

Subtract 36 from both sides:

x^2 = 100 - 36 = 64.

Take the square root and choose the positive length

To find $x$ , take the square root of both sides:

x = \pm \sqrt{64}.

Since a side length must be positive, $x = 8$ . The other leg of the triangle is 8 centimeters, which corresponds to answer choice C.

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Step-by-step Explanation

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Step-by-step Explanation