The document discusses the Law of Sines, which is a rule used to find unknown angles and sides of triangles when some combination of angles and sides are known. The Law of Sines states that the ratio of any side to its opposite angle is equal to the ratio of any other side to its opposite angle. An example problem demonstrates using the Law of Sines to solve a triangle when two angles and one side are given. Additional resources are provided to learn more about solving triangles with the Law of Sines.

1. Law of Sines

2. • 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?

3. 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.

4. Law of sines equation
sin A = sin B = sin C
a b c
Aforementioned equation can also be represented
in three different equations as shown below:
a = b = c
sin A sin B sin B

5. 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:

6. 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:

7. Let us first find the third angle,
Since =180°, we have = 180°- =180°-
35°-70°=75°.
Solution:

8. 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:

9. 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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