Sine & Cosine Rule & Area of Triangles Quiz

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

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

2. In a triangle, side $a = 10$ is opposite angle $A = 50°$, and angle $B = 70°$. Which rule finds side $b$?

• A. Cosine rule
• B. Sine rule
• C. Area formula
• D. Cannot be found

3. What is the area of a triangle with sides 8 cm and 12 cm and an included angle of 45°?

• A. 48 sin 45° cm²
• B. 24 sin 45° cm²
• C. 96 cm²
• D. 48 cm²

4. A triangle has sides $a=7$, $b=9$, $c=5$ (SSS). Which formula correctly finds angle $A$ (opposite side $a$)?

• A. $\cos A = \dfrac{b^2+c^2-a^2}{2bc}$
• B. $\sin A = \dfrac{a}{b}\sin B$
• C. $\cos A = \dfrac{a^2+b^2-c^2}{2ab}$
• D. $a^2 = b^2+c^2$

5. Using the sine rule with SSA data, solving $\sin\theta = 0.6$ gives a calculator angle of $36.9°$. If the other known angle is $30°$, which second value of $\theta$ must also be checked as a possible solution?

• A. 36.9°
• B. 180° − 36.9° = 143.1°
• C. 90° − 36.9° = 53.1°
• D. 360° − 36.9° = 323.1°