Question

in the right triangle with a right angle, one acute angle is 45°, another acute angle is 45°, the length of the right - angled side is 3, and the length of the hypotenuse is x. find the value of x.

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right isosceles triangle, so the two legs are equal. The given leg length is 3, so the other leg is also 3.

Step2: Apply Pythagorean theorem

Use $c^2 = a^2 + b^2$ where $a=3$, $b=3$, $c=x$.
$$x^2 = 3^2 + 3^2$$

Step3: Calculate $x^2$

$$x^2 = 9 + 9 = 18$$

Step4: Solve for $x$

Take the square root of both sides, simplify $\sqrt{18}$.
$$x = \sqrt{18} = 3\sqrt{2}$$

Answer:

$3\sqrt{2}$