Questions: Find the values of (x) and (y) in each of the following triangles. 1. (x=x quad y=x sqrt2) 2. (x=22.5 quad y=45)

Find the values of (x) and (y) in each of the following triangles.
1.
(x=x quad y=x sqrt2)
2.
(x=22.5 quad y=45)
Transcript text: Find the values of $x$ and $y$ in each of the following triangles. 1. \[ x=x \quad y=x \sqrt{2} \] 2. $x=22.5 \quad y=45$
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Solution

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Solution Steps

Step 1: Identify the type of triangle in Problem 1

The triangle in Problem 1 is a 45°-45°-90° triangle. In such triangles, the legs are congruent, and the hypotenuse is 2 \sqrt{2} times the length of each leg.

Step 2: Set up the relationship for Problem 1

Given that one leg is x x , the other leg is also x x , and the hypotenuse is x2 x\sqrt{2} .

Step 3: Solve for x x and y y in Problem 1

Since the hypotenuse is given as x2 x\sqrt{2} , we have: y=x2 y = x\sqrt{2}

Final Answer

For Problem 1: x=x x = x y=x2 y = x\sqrt{2}

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