Law of Sines and Cosines Knowledge-Based Practice

Questions

1. 1.

   In triangle $ABC$, the side lengths satisfy the equation $a^2 = b^2 + c^2 + bc$. What is the measure of angle $A$?

   • A) $120^\circ$
   • B) $60^\circ$
   • C) $135^\circ$
   • D) $150^\circ$
2. 2.

   In triangle $ABC$, side $a = 4\sqrt{2}$, side $b = 4$, and angle $A = 135^\circ$. What is the measure of angle $B$?

   • A) $15^\circ$
   • B) $45^\circ$
   • C) $60^\circ$
   • D) $30^\circ$
3. 3.

   In triangle $ABC$, the side lengths are $a = 5$, $b = 6$, and $c = 7$. What is the value of $\cos A$?

   • A) $\frac{1}{5}$
   • B) $\frac{19}{35}$
   • C) $\frac{5}{7}$
   • D) $-\frac{5}{7}$
4. 4.

   In triangle $ABC$, the interior angles are $A = 45^\circ$ and $B = 30^\circ$, and the side opposite angle $B$ has length $b = 10$. What is the length of side $a$?

   • A) $5\sqrt{2}$
   • B) $10\sqrt{2}$
   • C) $10\sqrt{3}$
   • D) $20\sqrt{2}$
5. 5.

   In triangle $ABC$, the side lengths are $a = 3$ and $b = 8$, and the measure of angle $C$ is $60^\circ$. What is the length of side $c$?

   • A) 5
   • B) $\sqrt{73}$
   • C) 7
   • D) $\sqrt{97}$

Answers and step-by-step solutions appear after you finish the test.