# Find angle of a triangle with given sides

• fork
In summary, to find the missing angle of a triangle with two given sides, you can use the law of cosines or the law of sines. However, you need to have at least one side and its corresponding opposite angle in order to use these equations. If you have all three sides of a triangle, you can use the law of cosines or the Pythagorean theorem to find the missing angle. There are also special cases, such as right triangles and equilateral triangles, where you can use simpler methods to find the missing angle.
fork
In a triangle ABC, AB=7, BC=8, CA=9, find angle B correct to 3 significant figures.
The answer is 73.4, but i don't know how to calculate it, thanks.

Use the cosine rule.

U'll need a calculator to compute B,i.e.solve the equation

$$\cos B=value$$

and select the first 3 decimals the calculator shows u...

Daniel.

O, I forgot there is a rule called " cosine rule" in the world, thanks.

The world hath many rules, none of which you ought to ignore..

## 1. How do I find the missing angle of a triangle with two given sides?

To find the missing angle of a triangle, you can use the law of cosines or the law of sines. The law of cosines states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the angle opposite the first side. The law of sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides. By rearranging these equations, you can solve for the missing angle.

## 2. Can I use any two sides of a triangle to find the missing angle?

No, in order to use the law of cosines or the law of sines, you need to have at least one side and its corresponding opposite angle. This means you need to have two sides and the angle between them, or two angles and the side between them. If you only have two sides and no angle, you cannot use these equations to find the missing angle.

## 3. What if I have all three sides of a triangle?

If you have all three sides of a triangle, you can use the law of cosines to find any of the angles. You can also use the Pythagorean theorem to find the missing angle if the triangle is a right triangle. However, if the triangle is not a right triangle, you will need to use the law of cosines.

## 4. Is there a formula for finding the missing angle of any triangle with given sides?

Yes, the law of cosines and the law of sines provide formulas for finding the missing angle of any triangle with given sides. However, these equations can be more complicated for certain types of triangles, such as obtuse or equilateral triangles. In those cases, it may be simpler to use other methods, such as the Pythagorean theorem or trigonometric functions.

## 5. Are there any special cases when finding the missing angle of a triangle with given sides?

Yes, there are special cases when finding the missing angle of a triangle. One common case is when the triangle is a right triangle, which means one of the angles is 90 degrees. In this case, you can use the Pythagorean theorem to find the missing angle. Another special case is when the triangle is an equilateral triangle, which means all three sides are equal and all three angles are 60 degrees. In this case, you can use simple geometry to find the missing angle.

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