A right triangle has legs measuring centimeters and centimeters. What is the length of the triangle's hypotenuse, in centimeters?

Solution available with step-by-step explanation

SAT Right Triangles & Trigonometry Question 28 | Free SAT Prep | Aniko

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Question 28·Easy·Right Triangles and Trigonometry

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A right triangle has legs measuring $8$ centimeters and $15$ centimeters. What is the length of the triangle's hypotenuse, in centimeters?

For right-triangle questions where two sides are given and you need the third, immediately think of the Pythagorean theorem $a^2 + b^2 = c^2$ . Identify which side is the hypotenuse (it is always opposite the right angle and is the longest side), plug in the given leg lengths, and solve for the missing side by adding the squares and taking a square root. On multiple-choice questions, you can also quickly check answers by squaring each option and seeing which one matches the sum of the squares of the legs, and eliminate any option that is shorter than a given leg (it cannot be the hypotenuse).

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Use the special property of right triangles

You are told the triangle is a right triangle. In such triangles, there is a specific relationship between the two legs and the hypotenuse. What theorem describes this relationship?

Write the equation with the correct sides

Let the legs be $a$ and $b$ and the hypotenuse be $c$ . Use $a^2 + b^2 = c^2$ and plug in 8 and 15 for the legs.

Solve step by step for the unknown side

After you compute $8^2$ and $15^2$ and add them, that sum equals $c^2$ . What operation do you use to go from $c^2$ to $c$ ?

Desmos Guide

Compute the hypotenuse using Pythagorean theorem

In a Desmos expression line, type sqrt(8^2 + 15^2). The value that Desmos returns is the length of the hypotenuse in centimeters.

Step-by-step Explanation

Identify the relevant formula

This is a right triangle, and you are given the lengths of the two legs (8 cm and 15 cm). To find the hypotenuse $c$ , use the Pythagorean theorem:

a^2 + b^2 = c^2

where $a$ and $b$ are the legs and $c$ is the hypotenuse (the side opposite the right angle).

Substitute the leg lengths and simplify

Let $a = 8$ and $b = 15$ :

8^2 + 15^2 = c^2 \\[0.7em] 64 + 225 = c^2 \\[0.7em] 289 = c^2

So the square of the hypotenuse is 289.

Take the square root to find the hypotenuse

To solve for $c$ , take the square root of both sides:

c = \sqrt{289}

Since $17 \times 17 = 289$ , $\sqrt{289} = 17$ . The hypotenuse is 17 centimeters, which corresponds to answer choice B.

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Step-by-step Explanation

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Step-by-step Explanation