3. Trigonometry

Law Of Cosines — Quiz

Test your understanding of law of cosines with 5 practice questions.

Practice Questions

Question 1

In a triangle $\triangle ABC$, if sides $a = 15$, $b = 20$, and angle $C = 70^\circ$, what is the length of side $c$ to two decimal places?

Question 2

Given a triangle with sides $a = 8$, $b = 12$, and $c = 15$, what is the measure of angle $B$ to the nearest degree?

Question 3

A triangular field has sides of length $150 \text{ m}$, $200 \text{ m}$, and $250 \text{ m}$. What is the measure of the angle opposite the longest side to the nearest degree?

Question 4

Two cars leave a junction at the same time. One travels at $60 \text{ km/h}$ and the other at $70 \text{ km/h}$. After $3$ hours, the angle between their paths is $50^\circ$. How far apart are the two cars to the nearest kilometer?

Question 5

In triangle $\triangle PQR$, if $p = 12$, $q = 18$, and $r = 20$, what is the value of $\cos(P)$?