Question

long leg2) Find the missing sides of the triangle. Leave your answers as simplified radicals. (2 points)60°√530

Answer 1

2√5 and √15

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):

`\begin{gathered} \sin\theta=\frac{\text{ opposite}}{\text{ hypotenuse}}=(o)/(h) \\ \\ \text{ we replacing} \\ \\ \sin30\degree=(√(5))/(h) \\ \\ h=(√(5))/(\sin30\degree) \\ \\ h=2√(5) \\ \\ \text{ now, for the adjacent side:} \\ \\ \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}=(o)/(a) \\ \\ \text{ we replacing} \\ \\ \tan30\degree=(√(5))/(a) \\ \\ a=(√(15))/(\tan30\degree) \\ \\ a=√(15)\: \end{gathered}`

Therefore, the value of the remaining sides is 2√5 for the hypotenuse and √15 for the other side.