Math  /  Geometry

QuestionQuestion
Find the length of the third side. If necessary, round to the nearest tenth.
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Studdy Solution

STEP 1

What is this asking? We've got a right triangle, we know the length of one leg and the hypotenuse, and we need to find the length of the other leg! Watch out! Don't mix up the legs and the hypotenuse in the Pythagorean theorem!

STEP 2

1. Set up the Pythagorean theorem.
2. Solve for the unknown side.

STEP 3

Alright, so the Pythagorean theorem says: a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the lengths of the legs, and cc is the length of the hypotenuse.

STEP 4

We know one leg is 1717, so let's call that a=17a = 17.
The hypotenuse is 2121, so c=21c = 21.
We want to find bb, the other leg.
Let's plug those values into our theorem: 172+b2=21217^2 + b^2 = 21^2

STEP 5

First, let's calculate those squares: 172=1717=28917^2 = 17 \cdot 17 = 289 and 212=2121=44121^2 = 21 \cdot 21 = 441.
So now our equation looks like this: 289+b2=441289 + b^2 = 441

STEP 6

To get b2b^2 by itself, we need to subtract 289289 from both sides of the equation.
Remember, what we do to one side, we *must* do to the other! 289289+b2=441289289 - 289 + b^2 = 441 - 289 b2=152b^2 = 152

STEP 7

Now, to find bb, we take the square root of both sides: b2=152\sqrt{b^2} = \sqrt{152} b=152b = \sqrt{152}

STEP 8

Since we're asked to round to the nearest tenth, we can approximate the square root of 152152. 15212.3\sqrt{152} \approx 12.3.
So, b12.3b \approx 12.3.

STEP 9

The length of the third side is approximately **12.3**.

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