ANSWER:
2√5 and √15
STEP-BY-STEP EXPLANATION:
We can calculate each side of the triangle by means of trigonometric ratios since it is a right triangle.
We must take into account the angle, we will use the 30° angle, that is, we know the side opposite the angle.
So we calculate each side as follows (adjacent side and hypotenuse):
[tex]\begin{gathered} \sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse}}=\frac{o}{h} \\ \\ \text{ we replacing} \\ \\ \sin30\degree=\frac{\sqrt{5}}{h} \\ \\ h=\frac{\sqrt{5}}{\sin30\degree} \\ \\ h=2\sqrt{5} \\ \\ \text{ now, for the adjacent side:} \\ \\ \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}=\frac{o}{a} \\ \\ \text{ we replacing} \\ \\ \tan30\degree=\frac{\sqrt{5}}{a} \\ \\ a=\frac{\sqrt{15}}{\tan30\degree} \\ \\ a=\sqrt{15}\: \end{gathered}[/tex]
Therefore, the value of the remaining sides is 2√5 for the hypotenuse and √15 for the other side.
