## When can law of sines be used?

The **law of sines can** be **used** to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It **can** also be **used** when two sides and one of the non-enclosed angles are known.

## How do you know when to use Sin Cos or tan?

**Sin** is equal to the side opposite the angle that you are conducting the functions on over the hypotenuse which is the longest side in the triangle. **Cos** is adjacent over hypotenuse. And **tan** is opposite over adjacent, which means **tan** is **sin**/**cos**.

## What is the main importance differences between using the law of sines and the law of cosines?

The **cosine** rule relates the **cosine** of an angle of a triangle to the sides of the triangle. With its help, the angles of a triangle can be determined, if all its sides are known. The **sine** rules gives the ratio of the **sine** of two angles of a triangle, which equals to the ratio of the corresponding opposite sides.

## What must you know to be able to use law of sines?

To **use** the **Law of Sines you** need to **know** either two angles and **one** side of the triangle (AAS or ASA) or two sides and an angle opposite **one** of them (SSA).

## What is the law of Triangle?

**Triangle law** of vector addition states that when two vectors are represented as two sides of the **triangle** with the order of magnitude and direction, then the third side of the **triangle** represents the magnitude and direction of the resultant vector.

## Does law of sines work for all triangles?

The **Sine** Rule **can** be used in any **triangle** (not just right-angled **triangles**) where a side and its opposite angle are known. You will only ever need two parts of the **Sine** Rule formula, not **all** three. Remember that each fraction in the **Sine** Rule formula should contain a side and its opposite angle.

## How is sin calculated?

In a right triangle, the **sine** of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the **sine** of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).

## How do you find sin given Cos?

Triangles! Patterns of right triangles. All triangles have 3 angles that add to 180 degrees. Therefore, if one angle is 90 degrees we can figure out **Sin** Theta = **Cos** (90 – Theta) and **Cos** Theta = **Sin** (90 – Theta).

## Is tangent sin over COS?

Today we discuss the four other trigonometric functions: **tangent**, **cotangent**, secant, and cosecant. Each of these functions are derived in some way from **sine** and **cosine**. The **tangent** of x is defined to be its **sine divided by** its **cosine**: **tan** x = **sin** x **cos** x.

## Why does the law of cosines work?

The **law of cosines** allows us to find angle (or side length) measurements for triangles other than right triangles. The third side in the example given would ONLY = 15 if the angle between the two sides was 90 degrees. In the example in the video, the angle between the two sides is NOT 90 degrees; it’s 87.

## What is the law of cosines and sines?

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.

## How do you 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)

## Is SAS law of cosines?

“**SAS**” is when we know two sides and the angle between them. use The **Law of Cosines** to calculate the unknown side, then use The **Law** of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

## What is the law of sines ambiguous case?

For those of you who need a reminder, the **ambiguous case** occurs when one uses the **law of sines** to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). If angle A is acute, and a = h, one possible triangle exists.

## How do you tell if there are two triangles law of sines?

Once you find the value of your angle, subtract it from 180° to find the possible second angle. Add the new angle to the original angle. **If their** sum is less than 180°, **you have two** valid answers. **If** the sum is over 180°, then the second angle is not valid.