2. Solve ∆ PQR in which ∠ P =116°, p = 8.3 cm and q = 5.4 cm.

To solve ∆ PQR, we are given that ∠ P = 116°, p = 8.3 cm, and q = 5.4 cm.

Step 1: Draw a triangle PQR with the given measurements. Label the angles and sides accordingly.

Step 2: Use the Law of Cosines to find the length of side r. The Law of Cosines states that c^2 = a^2 + b^2 - 2ab * cos(C), where c is the side opposite angle C. In this case, r is the side opposite angle R.

Using the Law of Cosines, we have: r^2 = p^2 + q^2 - 2pq * cos(P) r^2 = (8.3 cm)^2 + (5.4 cm)^2 - 2(8.3 cm)(5.4 cm) * cos(116°)

Step 3: Calculate the value of r^2 using the given measurements and the cosine of 116°.

Step 4: Take the square root of r^2 to find the length of side r.

Step 5: Now that we have the lengths of all three sides of the triangle, we can find the remaining angles using the Law of Sines or the Law of Cosines.

I hope this helps you solve ∆ PQR!