Question

find the length of side ( x ) to the nearest tenth.

(image of a right triangle with a right angle, one acute angle ( 45^circ ), the other acute angle ( 45^circ ), hypotenuse ( sqrt{6} ), and one leg labeled ( x ))

answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identificar triángulo y relación

Se trata de un triángulo rectángulo, usamos el seno:
$\sin(\theta) = \frac{\text{opuesto}}{\text{hipotenusa}}$

Step2: Sustituir valores conocidos

$\theta=45^\circ$, opuesto = $x$, hipotenusa = $\sqrt{6}$:
$\sin(45^\circ) = \frac{x}{\sqrt{6}}$

Step3: Despejar x y calcular

$\sin(45^\circ)=\frac{\sqrt{2}}{2}$, así que:
$x = \sqrt{6} \times \frac{\sqrt{2}}{2} = \frac{\sqrt{12}}{2} = \frac{2\sqrt{3}}{2} = \sqrt{3}$

Step4: Aproximar al décimo

$\sqrt{3} \approx 1.732$, redondeamos:
$x \approx 1.7$

Answer:

$x = 1.7$