Use Special Right Triangles to Solve for the Exact Value of x

To find the exact value of x using special right triangles, we first need to identify the relevant special triangles and how they relate to the given problem.

Special right triangles include the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the sides are in the ratio of 1:1:√2. In a 30-60-90 triangle, the sides are in the ratio of 1:√3:2.

Let’s assume we are trying to find x in a right triangle context, where x could represent a side length or an angle. If we have a 45-45-90 triangle, and one leg measures 1, then the other leg will also measure 1, and the hypotenuse will be √2. So, if x is the length of the hypotenuse, then:

  • Hypotenuse (x) = 1 × √2 = √2

If we were dealing with a 30-60-90 triangle, and we know one angle is 30 degrees, let’s say the shortest side opposite the 30-degree angle is 1. Then, using the ratios, the side opposite the 60-degree angle would be √3, and the hypotenuse will be 2. If x represents the hypotenuse in this scenario, then:

  • Hypotenuse (x) = 2

In both cases, we utilized the properties and ratios of special right triangles to solve for x directly. Therefore, to determine the exact value of x, you need to identify which triangle properties fit the given measurements of your triangle.

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