Contents

- 1 How do you know when to use the law of sines or cosines?
- 2 How is law of cosine used in real life?
- 3 When can cosine rule be used?
- 4 Does law of cosines work for right triangles?
- 5 When can you not use the law of sines?
- 6 How do you use the law of sines and cosines to solve a triangle?
- 7 Is Pythagorean theorem only for right triangles?
- 8 How do you remember the cosine rule?
- 9 What are the law of sines and cosines?
- 10 What do you need to use the law of cosines?
- 11 What does the law of cosines reduce to?
- 12 Which type of triangles does law of cosines work best on?

## How do you know when to use the law of sines or cosines?

The **sine** rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The **cosine** rule is used when we are given either a) three sides or b) two sides and the included angle.

## How is law of cosine used in real life?

The **law of cosines** is **used** in the **real world** by surveyors to find the missing side of a triangle, where the other two sides are known and the angle opposite the unknown side is known. To use the **law of cosines** formula, we simply plug in our two known sides into a and b, and then our angle into C.

## When can cosine rule be used?

The **Cosine Rule can** be **used** in any triangle where you are trying to relate all three sides to one angle. If you need to find the length of a side, you need to know the other two sides and the opposite angle. Side a is the one you are trying to find.

## Does law of cosines work for right triangles?

In this case the tool is useful when you know two sides and their included angle. From that, you **can** use the **Law of Cosines** to find the third side. It works on any **triangle**, not just **right triangles**.

## When can you not use the law of sines?

**If we** are given two sides and an included angle of a triangle or **if we** are given 3 sides of a triangle, **we** cannot **use the Law of Sines** because **we** cannot set up any proportions where enough information is known.

## How do you use the law of sines and cosines to solve a triangle?

This means we are given two sides and the included angle. For this type of **triangle**, we must **use** The **Law** of **Cosines** first to calculate the third side of the **triangle**; then we can **use** The **Law of Sines** to find one of the other two angles, and finally **use** Angles of a **Triangle** to find the last angle.

## Is Pythagorean theorem only for right triangles?

**Pythagoras**‘ **theorem only** works for **right**-angled **triangles**, so you can use it to test whether a **triangle** has a **right** angle or not. In the **triangle** above, if a 2 < b 2 + c 2 the angle is acute.

## How do you remember the cosine rule?

You only need to **remember** the +2abcos(C) bit. Yep. It’s rearranged to resemble Pythagoras’s **formula**.

## What are the law of sines and cosines?

The **Law of Sines** establishes a relationship between the angles and the side lengths of ΔABC: a/sin(A) = b/sin(B) = c/sin(C). This is a manifestation of the fact that **cosine**, unlike **sine**, changes its sign in the range 0° – 180° of valid angles of a triangle.

## What do you need to use the law of cosines?

When to **Use**

The **Law of Cosines** is useful for finding: the third side of a triangle when **we** know two sides and the angle between them (like the example above) the angles of a triangle when **we** know all three sides (as in the following example)

## What does the law of cosines reduce to?

The **Law of Cosines** applies to any triangle with side lengths a,b,c and angles A,B,C. Note that if C is a right angle, then cos(C) = 0 and the **law of cosines** reduces to the Pythagorean Theorem: a^{2} + b^{2} = c^{2}.

## Which type of triangles does law of cosines work best on?

The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two **sides** and the measure of the included **angle** is known (SAS) or the lengths of the three **sides** (SSS) are known.