Law of Sines and Cosines Knowledge-Based Download PDF

Questions

1. 1.

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

   • A) $60^\circ$
   • B) $90^\circ$
   • C) $120^\circ$
   • D) $150^\circ$
2. 2.

   In triangle $ABC$, side $a = 6$, side $b = 6\sqrt{3}$, and the measure of angle $A$ is $30^\circ$. Given that angle $B$ is obtuse, what is the measure of angle $B$?

   • A) $120^\circ$
   • B) $60^\circ$
   • C) $135^\circ$
   • D) $150^\circ$
3. 3.

   In triangle $ABC$, the side lengths are $a = 3$, $b = 5$, and $c = 7$. What is the measure of angle $C$?

   • A) $60^\circ$
   • B) $120^\circ$
   • C) $135^\circ$
   • D) $150^\circ$
4. 4.

   In triangle $ABC$, the measure of angle $A$ is $45^\circ$, the measure of angle $B$ is $30^\circ$, and side $b = 8$. What is the length of side $a$?

   • A) $4\sqrt{2}$
   • B) $8\sqrt{3}$
   • C) 16
   • D) $8\sqrt{2}$
5. 5.

   In triangle $ABC$, the side lengths are $a = 5$ and $b = 8$, and the measure of angle $C$ is $60^\circ$. What is the length of side $c$?

   • A) $\sqrt{69}$
   • B) $\sqrt{89}$
   • C) 7
   • D) $\sqrt{129}$