Question

Find the missing sides of the following without using calculator

Answer 1

Answer:

The missing sides are 3 and 3√3

Explanation:

Let the opposite sides be represented by x, and the other missing side be y, then

$\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}$

Using the above, we have:

$\begin{gathered} \sin 60=\frac{x}{6} \\ \\ x=6\sin 60 \\ =6\times\frac{\sqrt[]{3}}{2} \\ \\ =3\sqrt[]{3} \end{gathered}$

And

$\begin{gathered} \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \\ \cos 60=\frac{y}{6} \\ \\ y=6\cos 60 \\ =6\times\frac{1}{2} \\ \\ =3 \end{gathered}$

The missing sides are 3 and 3√3