## What are the 3 formulas for the Law of Cosines?

Important Notes on Law of Cosines:

- Three different versions of the law of cosine are: a2 = b2 + c2 – 2bc·cosA. b2 = c2 + a2 – 2ca·cosB. c2 = a2 + b2 – 2ab·cosC.
- Pythagoras Theorem is a generalization of the Law of Cosine.
- The law of cosine can be applied in any triangle.

## How do you find out the area of a triangle?

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

**What is the cosine of a triangle?**

In any right triangle, the cosine of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H). In a formula, it is written simply as ‘cos’.

### Which Triangle’s area can be calculated using?

The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

### How do you find an area of a triangle?

**How do you find the area of a triangle using TRIG?**

The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. AreaΔ = ½ ab sin C. You may see this referred to as the SAS formula for the area of a triangle.

#### How do we find area of a triangle?

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.

#### When can you use law of cosines?

To solve a triangle is to find the lengths of each of its sides and all its angles. 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.

**Why is the area of a triangle 1 2BH?**

Observe that, if we cut this parallelogram by half, and remove this portion, we now have a triangle with the base B and height H. Since the area of this triangle, is half of the area of a parallelogram, the formula for the area of this triangle, A = 1/2BH.

## What is the law of cosines for triangles?

Law of Cosines: (for all triangles) a2 + b2 − 2ab cos (C) = c2 So, to remember it: think ” abc “: a2 + b2 = c2,

## How do you use the law of cosines to find area?

How do you use the law of cosines to find the area of a triangle? The law of cosines is useful when you know two sides and the angle between them, or when you know all three sides. Lets take a look at a generic triangle, ABC;

**How do you find the cosine of a triangle?**

Law of cosines formula The law of cosines states that, for a triangle with sides and angles denoted with symbols as illustrated above, a² = b² + c² – 2bc * cos (α) b² = a² + c² – 2ac * cos (β) c² = a² + b² – 2ab * cos (γ) For a right triangle, the angle gamma, which is the angle between legs a and b, is equal to 90°.

### How do you derive the law of cosines from an analogous equation?

Analogical equations may be derived for other two sides: To finish the law of cosines proof, you need to add the equation (1) and (2) and subtract (3): a² + b² – c² = ac * cos (β) + ab * cos (γ) + bc * cos (α) + ab * cos (γ) – bc * cos (α) – ac * cos (β)