# Law of Sines and Cosines Word Problems Worksheet (with Answer Key + PDF)

Law of sines and law of cosines in trigonometry are important rules used for solving a triangle. In this worksheet, you will learn about solving word problems through the law of sines and cosines.

## What is “Law of Sines”?

The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data. The sine law can be defined as

The Law of Sines can also be written in the reciprocal form

## What is the “Law of Cosines”?

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The law of cosine can be represented as

## How will the “Law of Sines and Cosines Word Problems Worksheet ” help you?

This worksheet will help you to solve the word problems through the law of sines and cosines.

## Instructions on how to use the “Law of Sines and Cosines Word Problems Worksheet (with Answer Key + PDF) ”

Use this math worksheet to carefully study the concepts for law of sines and cosines word problems.

A 10-item activity is given after the lesson in order to exercise the learned concept.

Towards the end of this worksheet, a reflective section is provided in order to help the learner think about their own thinking (metacognition) and assess how they performed in the lesson.

## Conclusion

At the end of this worksheet, the learner will effectively learn about solving the word problems through the law of sines and cosines.