In a right triangle, one leg is x, the other leg is 13, and the hypotenuse is 26. F...
Check the final answer first, then review the worked steps.
Problem
In a right triangle, one leg is x, the other leg is 13, and the hypotenuse is 26. Find the approximate value of x.
Answer
22.52 units
Step-by-step solution
- Identify the problem type: This is a geometry problem involving a right triangle.
- Recognize the relationship between sides: The image shows a right triangle with legs of length $x$ and $13$, and a hypotenuse of length $26$. The Pythagorean theorem relates the lengths of the sides of a right triangle: $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.
- Apply the Pythagorean theorem: Substitute the given values into the theorem: $x^2 + 13^2 = 26^2$.
- Calculate the squares: $13^2 = 169$ and $26^2 = 676$. The equation becomes $x^2 + 169 = 676$.
- Isolate $x^2$: Subtract $169$ from both sides of the equation: $x^2 = 676 - 169$.
- Perform the subtraction: $x^2 = 507$.
- Solve for $x$: Take the square root of both sides: $x = \sqrt{507}$.
- Calculate the approximate value of $x$: Using a calculator, $\sqrt{507} \approx 22.51666$. Rounding to two decimal places, $x \approx 22.52$.