When given **SAS** or **SSS quantities**, use the **law of cosines**. This would be **SAS** if you were given the lengths of sides b and c, as well as the measure of angle A. When we know the lengths of the three sides a, b, and c, we call it **SSS**.

Similarly, When should you use law of cosines?

To **solve a triangle**, you must **determine the lengths** of all of its **sides** and angles. When we are given a) two angles and one side, or b) two **sides** and a non-included angle, we **utilize** the sine rule. When we are provided either a) three **sides** or b) two **sides** and the included angle, we **utilize** the cosine rule.

Also, it is asked, What cases need to use law of cosines?

When Should You Use It? When we know two **sides** and the angle between them, we may apply the **Law of Cosines** to get the third side of a **triangle** (like the example above) When we know all three **sides** of a **triangle**, we may calculate its angles (as in the following example)

Secondly, When can the law of sines be used?

When we know two **angles** and one side or two **angles** and one **included side**, we usually utilize the **law of sines** to **solve the triangle**. When we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria, the **law of sines** may be used.

Also, What is the difference between law of sines and law of cosines?

The **sines** of the angle and the **side opposite** it are related by the **rule of sines**. The **angle opposing** a **side** is also used in the law of cosines. With the proper set of inputs, they may both be used to calculate the length of a triangle’s **side** or one of its angles.

People also ask, In which of the following situation will the law of cosine be applied?

The **Cosine Rule** may be applied to any triangle in which all three sides must be related to one **angle**. You’ll need to know the other two sides as well as the **opposite angle** to calculate the length of a side.

Related Questions and Answers

## Can the Law of Cosines be applied to right triangles?

Any **triangle**, not **simply right triangles**, may be used. where a and b are the two provided sides, C is their **included angle**, and c is the third side that is unknown. See the diagram above.

## What 2 cases can the Law of Sines be used?

When Should the **Law of Sines** Be Used? When Angle-Side-Angle (**ASA**) or Angle-Angle-Side (AAS) congruency exists, the **Law of Sines** is applied. In fact, in our next lesson, titled the **Ambiguous Case**, we’ll learn about another form of congruency that the **Law of Sines** may be applied to.

## Can you always use Law of Sines?

The law of **sines formula enables** us to **calculate a percentage** of opposing sides/angles (technically, you’re really taking the sine of an angle and its opposite side) When should the law of **sines formula** be used? What you’re aware ofWhat you’re able to locate 2 angles and the sideside opposite the known angle that is not included

## Which case Cannot be solved using laws of sines?

We cannot utilize the **Law of Sines** if we are given two sides and an **included angle** of a triangle, or if we are given three sides of a triangle, since we cannot build up any proportions where adequate **information is provided**. In these two circumstances, the **Law of Cosines** must be applied.

## Which of the following best describes the law of cosines?

The **Law of Cosines** is best described by which of the following **phrases**? The total of the squares of the remaining two sides, minus twice the product of the two **remaining sides** and the cosine of the angle between them, **equals the square** of any side of a triangle. You’ve only gone through 5 terms!

## Why do we need sine and cosine?

It may **assist** us in better **comprehending the relationships** between **rectangle sides** and angles. In the study of right triangles, the terms sine, cosine, and tangent are crucial. Have you ever seen a triangle like this before? If that’s the case, you’re aware that one of the three angles is always 90 degrees (a right angle).

## What is meant by cosine law?

The **square** of a side of a **planar triangle** is the total of the squares of the other **sides minus** twice the product of those **sides** and the cosine of the angle between them, according to the **law of cosines** 1.

## Which law should be applied if three sides of a triangle are given?

**SSS**: If you know the three sides of a triangle, apply the **Law of Cosines** to determine one of the angles. It’s normally better to start with the greatest angle, which is the one on the opposite side of the longest side. Then, to get the second angle, build up a proportion using the **Law of Sines**.

## In which of these cases can we use the law of sines to solve the triangle?

Applying the **Law of Sines**: As long as two of the angles and one of the sides are known, the **Law of Sines** may be used to **solve for missing** lengths or angle measurements in an **oblique triangle**.

## Why can’t you solve this triangle using the law of sines?

Because we need to know at least one angle and the **opposite side** to solve an **SAS triangle**, we can’t utilize the **Law of Sines** in the first step.

## Can you use law of sines on obtuse triangles?

The sine **rule also applies** to **obtuse-angled triangles**: = for an **obtuse-angled** triangle. To compute the sine and cosine of the angles 0°, 90°, and 180°, we may utilize the expanded definition of trigonometric functions.

## Why does sine rule not work?

When the three sides of a triangle are known, the three angles may be **calculated individually**. (The **SSS congruence test** is used here.) We may use the cosine rule instead of the **sine rule** to calculate the three angles since the **sine rule** needs knowledge of (at least) one angle.

## Can the law of cosines be used to solve any triangle for which two angles and a side are known explain your answer?

When the **lengths** of two sides and the measure of the **included angle** (SAS) or the **lengths** of the three sides (SSS) are known, the **Law of Cosines** is used to **identify the remaining** components of an oblique (non-right) triangle.

## Is the Pythagorean theorem a special case of the law of cosines?

Because cos (**theta**) = 0 when the angle is a 90 degree or right angle, the **Pythagorean Theorem** is a **specific instance** of the **law of cosines**, a2 + b2 – 2*a*b*cos (**theta**) = c2. We also discovered that the Pythagorean Theorem’s inverse is correct.

## Can you solve SSS with law of sines?

To solve a triangle, you must first determine all of the angles and **side lengths**. The **Law of Sines** is a useful technique for **resolving triangles**, but it requires the knowledge of an angle and its opposite side. As a result, the **Law of Sines** cannot be utilized to **solve SSS** (side-side-side) or SAS (side-angle-side) configurations as a first step.

## Can you solve SAS with law of sines?

When we know two sides and the angle between them, we call it “**SAS**.” Calculate the **unknown side** using The **Law of Cosines**, then determine the lesser of the other two angles using The **Law of Sines**, and then add the three angles to 180° to obtain the last angle.

## Which of the following cases where we can use the law of cosines in solving oblique triangles?

When two sides and their included **angle are supplied**, and when three sides are given, this **rule is employed** largely in two circumstances. When two sides and their included angles are known, the third side must be calculated. As illustrated above, the **Law of Cosines** is ideal for the circumstance.

## Why do we need sine?

As we’ve seen, sine is one of the most **important trigonometric functions**, and it’s defined as the ratio of the opposite angle’s side divided by the hypotenuse. It’s useful for calculating distances and heights, and it can also be used to calculate angle measurements in radians.

## Conclusion

The “when to use law of sines” is a trigonometric function that can be used in many different scenarios. The Law of Sines is best used when the side lengths are known.

This Video Should Help:

The “law of cosines to find angle” is a trigonometric equation that can be used to find the angle between two lines.

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