Law of Sines

• The law of sines is a rule that is used in finding the angles of general triangles.

• This law is applicable where two sides of a triangle and the angle opposite one of them are given.

• In such a case, the angle opposite the other side of the triangle can be calculated using law of sines.

• The law specifies that the sum of the interior angles of a triangle must equal to 180 degrees. The third angle can easily be determined then.

What is law of sines?

Law of sines equation

Assume that the side ‘a’ of a triangle is opposite angle A, the side ‘b’ is opposite angle B, and the side ‘c’ is opposite angle C. 

Law of sines equation

sin A      =     sin B         =      sin C a b cAforementioned equation can also be represented in three different equations as shown below:a = b = csin A sin B sin B

It is proven that in a single triangle the ratio of each side to its corresponding opposite angle is equal to the ratio of any other side to its corresponding angle.

Law of Sines States:

Use the Law of Sines to solve the following ASA Triangle.

= 35°,   b = 5,    =70°. The side of the triangle and two its adjacent angles are given.

Example:

Let us first find the third angle,

Since =180°, we have    = 180°- =180°-35°-70°=75°.

 

Solution:

Next, we shall calculate side a using Law of Sine with known side b and angles    and   : 

= b*sin(35°)/sin(75°) = 5*0.574/0.966 = 2.969. 

Solution:

Now, we will calculate side c using Law of Sine with known side b and angles   and   : 

=> b*sin(70°)/sin(75°) = 5*0.940/0.966 = 4.864.

Solution:

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