Free printable worksheet

Law of Sines and Cosines Worksheet

Twelve Law of Sines and Law of Cosines problems with labeled non-right triangles.

PrecalculusGrades 10-124 pagesAnswer key included

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What this worksheet includes

  • Twelve Law of Sines and Law of Cosines problems with labeled non-right triangles.
  • 4-page printable PDF with a complete answer key
  • Designed for Grades 10-12 precalculus practice
  • First-page preview available before the free email unlock

How to use it

Use this law of sines and cosines worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.

After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.

Who this practice is for

This resource is designed for grades 10-12 students working on precalculus. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.

Looking for a broader sequence? Browse all Precalculus worksheets.

Topic guide

How to approach law of sines and cosines

Law of Sines and Cosines practice is most effective when students identify the governing definition, theorem, or rule before beginning a calculation. Twelve Law of Sines and Law of Cosines problems with labeled non-right triangles.

This precalculus set moves from direct applications into mixed review. Students should preserve exact values, label each important step, and use the answer key to locate the first point where an incorrect solution changes direction.

Learning objectives

  • Recognize the central rules and representations used in law of sines and cosines
  • Apply an efficient procedure to solve law of sines and cosines problems
  • Check results using notation, substitution, estimation, or a relevant inverse process

Skills to review first

  • Core vocabulary connected to law of sines and cosines
  • Accurate arithmetic and algebraic simplification
  • Reading mathematical notation and showing work in a logical sequence
Worked example

Follow the reasoning step by step

Plan and solve a representative law of sines and cosines problem from Part A.

  1. List the given information and state what must be found.
  2. Select the definition, theorem, formula, or procedure that applies to law of sines and cosines.
  3. Substitute or transform carefully, keeping one logical change on each line.
  4. Check the result against the original conditions and include units or restrictions when needed.

Solution: A complete solution includes the correct result and enough reasoning to verify it.

Try before downloading

Three sample problems

Work each problem, then open the answer to check your result.

Problem 1 · foundations

Given A=30∘, B=45∘, a=8A=30^\circ,\ B=45^\circ,\ a=8, use the Law of Sines to find bb.

Triangle ABC with angle A 30 degrees, angle B 45 degrees, side a 8, and side b unknownABCca = 8b = ?30°45°
Show answer

828\sqrt2

Problem 2 · skill practice

Given a=5, b=7, C=60∘a=5,\ b=7,\ C=60^\circ, use the Law of Cosines to find cc.

Triangle ABC with sides a 5 and b 7, included angle C 60 degrees, and side c unknownABCc = ?a = 5b = 760°
Show answer

39\sqrt{39}

Problem 3 · mixed review

Given A=70∘, a=4, b=9A=70^\circ,\ a=4,\ b=9, determine whether 0, 1, or 2 triangles are possible.

Hypothetical triangle ABC with angle A 70 degrees, side a 4, and side b 9ABCc = ?a = 4b = 970°
Show answer

00

Error check

Common mistakes to watch for

  • Beginning a calculation before identifying the relevant rule or given information
  • Dropping a sign, unit, restriction, or exact-value symbol during simplification
  • Comparing only the final answer instead of checking the first incorrect step
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