# Thread: Trigonometry: Sine and Cosine Law

1. ## Trigonometry: Sine and Cosine Law

Topic is for those who kept looking for information about the law of sines and cosines.

Sine law:

Where a, b, c are the sides of the triangle.

Cosine law:

Let's check this on some exercises:

1) Solve the triangle where

The best practice is to draw the triangle and mark our known angles and sides.

We know two sides and angle between them.
To find length of side a we have to use the Cosine Law:

To count B angle we need to use the Cosine law:

To count angle C we have to use simple formulae. As we know sum of angles in triangle is equal to 180°.

Answer: Angles- and Sides-

2. When we have to find the angle in a triangle using the law of Sine, the best practice is to turn the fraction upside down.

Let's do some exercise:

Determine the remaining angles:

To find out angle C I'am going to use Sine law. I've angle B=80° and length of sides b=4 and c=3

Now sum of all angles in triangle is equal to 180. We know two of them so we can simply count the third one.

For more practice we can find out the length of side a, using also the Sine law.

Answer: A=52.38 B=80° C=47.61° a=3.21 b= 4 c=3

3. In this exercise, I will use Cosine law to find out one of the angles in triangle.

Firs we have to determine length of sitde b. We need this side to count angle C.

Now we can find C by Cosine law.

Ok now we have to find angle A so:

Answer: A=98.48° B=26° C=55.52°

4. More complex exercise where we can apply law of Sine and Cosine.

The crank mechanism shown below has an arm OA of length 30mm rotating anticlockwise about O and connecting rod AB of length 60mm. B moves along the horizontal line OB. What is the length OB when OA is rotated by of a complete revolution from the horizontal.

So as we know full revolution is equal to 360°. To resolve this exercise we have to find angle of side OA with OB in of the mechanism revolution. So after calculation we have found that our angle of OA and OB is equal to 45°.

To don't get confused the best practise it will be to draw simple triangle and find our sides and angle which we know so far.

So first step it will be to find what angle C=B is equal to. To do that we have to use the Sine law. I will turn the fraction upside down to make it easer.

As always to count third angle we have to use formulea: A+B+C=180°

To find our unknown a=OB we can use the Sine law.

Answer: OB=77.31cm

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•
###### About us
Website refrigeration.engineering has been designed for you. That is our passion to connect people with common interest in engendering. We wish you to have good time on the board.