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For the following right triangle, find the side length
x. Round your answer to the nearest hundredth.

For the following right triangle, find the side length $x$ . Round your answer to the nearest hundredth.

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Find missing angles in special triangles

Full solution

Q. For the following right triangle, find the side length

x

. Round your answer to the nearest hundredth.

Use Pythagorean Theorem: Use Pythagorean theorem: $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse and $a$ , $b$ are the other two sides.
Given Side Lengths: Let's say we know the lengths of the other two sides, for example, $a = 5$ cm and $c$ (hypotenuse) = $13$ cm. We need to find $b$ which is $x$ in this case.
Plug in Values: Plug the known values into the Pythagorean theorem: $5^2 + x^2 = 13^2$ .
Calculate Squares: Calculate the squares: $25 + x^2 = 169$ .
Isolate $x^2$ : Subtract $25$ from both sides to isolate $x^2$ : $x^2 = 169 - 25$ .
Calculate Difference: Calculate the difference: $x^2 = 144$ .
Solve for x: Take the square root of both sides to solve for x: $x = \sqrt{144}.$
Final Calculation: Calculate the square root: $x = \sqrt{12}$ .

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