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

Solution available with step-by-step explanation

SAT Right Triangles & Trigonometry Question 1 | Free SAT Prep | Aniko

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Question 1·Easy·Right Triangles and Trigonometry

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

When you see a right triangle with two sides given, immediately think of the Pythagorean theorem $a^2 + b^2 = c^2$ , making sure you correctly identify the hypotenuse as $c$ . Plug in the known values, solve the simple equation for the unknown side, and only then take the square root at the end. With practice, you’ll also recognize common Pythagorean triples like $6$ – $8$ – $10$ , which lets you answer questions like this even faster without full calculation.

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Recall the key formula

For a right triangle, what equation relates the lengths of the two legs and the hypotenuse?

Identify which side is which

Which given side is the hypotenuse (the longest side, opposite the right angle), and which is a leg?

Set up and solve the equation

Let $x$ be the unknown leg. Substitute $6$ for one leg and $10$ for the hypotenuse into the Pythagorean theorem, then solve for $x$ .

Desmos Guide

Use Desmos to compute the missing leg

In Desmos, type sqrt(10^2 - 6^2) and look at the numeric output. That value is the length of the missing leg.

Step-by-step Explanation

Identify the known and unknown sides

You are told the triangle is a right triangle. The side of length $10$ inches is the hypotenuse (the side opposite the right angle), and the side of length $6$ inches is one leg. Let $x$ be the length of the other leg.

Write the Pythagorean theorem for this triangle

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

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

Here, the legs are $6$ and $x$ , and the hypotenuse is $10$ , so

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

Now simplify both squares.

Solve for the unknown leg

Compute the squares:

6^2 = 36, \quad 10^2 = 100.

So the equation becomes

36 + x^2 = 100.

Subtract $36$ from both sides:

x^2 = 100 - 36 = 64.

Take the positive square root (side lengths are positive):

x = \sqrt{64} = 8.

So the other leg of the triangle is $8$ inches long, which corresponds to choice B.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation