Construct a triangle PQR such that PQ=6cm and angle PQR=70 degrees. Construct the perpendicular bisector by setter of lpal and draw a circle with O as centre and lpal.

Okay, Ella, let's measure the radius of the circumcircle.

Step 1: Measure the radius of the circumcircle

• On your construction, place the ruler with one end at point $O$ (the center of the circumcircle).
• Measure the distance from $O$ to any of the vertices $P$, $Q$, or $R$. This distance is the radius of the circumcircle. For example, measure the length of $OP$.

The theoretical value for the circumradius ($R$) can be calculated using the Law of Sines:

$$R = \frac{a}{2\sin A} = \frac{b}{2\sin B} = \frac{c}{2\sin C}$$

Using the side $RP$ (which we calculated as approximately $5.97 \text{ cm}$) and the angle opposite to it, $\angle PQR = 70^\circ$:

$$R = \frac{RP}{2\sin(\angle PQR)}$$ $$R = \frac{5.97 \text{ cm}}{2\sin(70^\circ)}$$ $$R = \frac{5.97 \text{ cm}}{2 \times 0.9397}$$ $$R = \frac{5.97 \text{ cm}}{1.8794}$$ $$R \approx \boxed{3.18 \text{ cm}}$$

Your measured value should be close to this.