Sine, Cosine Rule & Area of Triangles Quiz

1. Which rule should you use if you know two sides of a triangle and the angle between them, and want to find the third side?

• A. Cosine rule
• B. Sine rule
• C. Pythagoras' theorem
• D. Area formula

2. In a triangle, $A=50°$, $a=10$ cm, $B=70°$. Find side $b$.

• A. 12.3 cm
• B. 10.9 cm
• C. 13.0 cm
• D. 9.4 cm

3. A triangle has sides $b=6$, $c=8$ and included angle $A=90°$. What is the area?

• A. 24
• B. 48
• C. 14
• D. 28

4. Why can the sine rule give an 'ambiguous case' when finding an angle?

• A. Because sine is positive for both an angle and its supplement (180° minus the angle)
• B. Because sine is always negative for obtuse angles
• C. Because cosine and sine give the same value
• D. Because the sine rule cannot be rearranged for angles

5. Triangle sides $a=7$, $b=9$, $c=5$. Using the cosine rule, is the angle opposite side $b$ (angle $B$) acute or obtuse?

• A. Obtuse, since $\cos B$ comes out negative
• B. Acute, since $\cos B$ comes out positive
• C. Cannot be determined without more information
• D. Exactly 90 degrees, since $\cos B = 0$