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)

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

Solution

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 $\sqrt{2}$ times the length of each leg.

Step 2: Set up the relationship for Problem 1

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

Step 3: Solve for

x

and

y

in Problem 1

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

Final Answer

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

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