Table of contents

0. Review of College Algebra(0)
1. Measuring Angles(0)
2. Trigonometric Functions on Right Triangles(0)
3. Unit Circle(0)
4. Graphing Trigonometric Functions(0)
5. Inverse Trigonometric Functions and Basic Trigonometric Equations(0)
6. Trigonometric Identities and More Equations(0)
7. Non-Right Triangles(0)
8. Vectors(0)
9. Polar Equations(0)
10. Parametric Equations(0)
11. Graphing Complex Numbers(0)

7. Non-Right Triangles

Law of Cosines

7. Non-Right Triangles

Law of Cosines - Online Tutor, Practice Problems & Exam Prep

Law of Cosines Practice Problems

40 problems

1PRACTICE PROBLEM

Find the missing side lengths and angles of the triangle. Express the lengths and angles in one decimal place.

2PRACTICE PROBLEM

Given the vertices of a triangle, determine the lengths of all its sides and measure all its angles. Round the side lengths and the angles to one decimal place.

A(- 2, 0), B(- 6, 5), C(4, - 2)

3PRACTICE PROBLEM

Find the solution for the following triangle given the measurement of one angle and two sides. If there is no possible triangle, indicate "no triangle," and if two triangles exist, solve each one. Round the resulting angle and side measurements to one decimal place.

C = 71°, a = 19, b = 9

4PRACTICE PROBLEM

B = 143°, a = 13.9, c = 55.6

5PRACTICE PROBLEM

Calculate the area of the triangle provided the following side lengths. Express the result to two decimal places.

a = 11 inches, b = 18 inches, c = 23 inches

6PRACTICE PROBLEM

Using the law of cosines, calculate the measure of z given the following measurements for the oblique triangle XYZ. Round the answer to two decimal places.

Z = 87°, x = 11 ft, y = 17 ft

7PRACTICE PROBLEM

Calculate the area of the triangle provided the following side lengths. Express the result to two decimal places.

a = 19 ft, b = 19 ft, c = 19 ft

8PRACTICE PROBLEM

Find the missing side lengths and angles of the triangle. Express the lengths to one decimal place and the angle to the nearest degree.

p = 6, q = 9, r = 13

9PRACTICE PROBLEM

For the given triangle, determine the area of the triangle using Heron's formula and report the area rounded to the nearest square unit.

p = 21 feet, q = 16 feet, r = 6 feet

10PRACTICE PROBLEM

Find the missing side length and angles of the triangle. Express the length to one decimal place and the angle to the nearest degree.

11PRACTICE PROBLEM

Find the missing angles of the triangle. Express the angle to the nearest degree.

12PRACTICE PROBLEM

Find the missing side length and angles of the triangle. Express the length to one decimal place and the angle to the nearest degree.

p = 9, q = 8, R = 72°

13PRACTICE PROBLEM

Find the missing side length and angles of the triangle. Express the length to one decimal place and the angle to the nearest degree.

q = 6, r = 2, P = 38°

14PRACTICE PROBLEM

Find the missing side length and angles of the triangle. Express the lengths to one decimal place and the angle to the nearest degree.

p = 7, r = 3, Q = 40°

15PRACTICE PROBLEM

Find the missing side length and angles of the triangle. Express the length to one decimal place and the angle to the nearest degree.

p = 9, r = 4, Q = 90°

16PRACTICE PROBLEM

Find the missing angles of the triangle. Express the angle to the nearest degree.

p = 4, q = 7, r = 10

17PRACTICE PROBLEM

Find the missing angles of the triangle. Express the angle to the nearest degree.

p = 24, q = 24, r = 24

18PRACTICE PROBLEM

Find the missing angles of the triangle. Express the angle to the nearest degree.

p = 24, q = 75, r = 58

19PRACTICE PROBLEM

For the given triangle, determine the area of the triangle using Heron's formula and report the area rounded to the nearest square unit.

p = 12 m, q = 12 m, r = 2 m

20PRACTICE PROBLEM

For the given triangle, determine the area of the triangle using Heron's formula and report the area rounded to the nearest square unit.

p = 24 cm, q = 15 cm, r = 11 cm

21PRACTICE PROBLEM

Let a triangle be labeled as PQR.

For the given measurements, find out if SAA, SAS, ASA, SSA, or SSS is given. Also, state the law which is suitable for solving the triangle.

P, Q, and r

22PRACTICE PROBLEM

Let a triangle be labeled as PQR.

For the given measurements, find out if SAA, SAS, ASA, SSA, or SSS is given. Also, state the law which is suitable for solving the triangle.

p, q, and R

23PRACTICE PROBLEM

Determine the missing side length of the triangle.