The document discusses trigonometric methods for solving oblique triangles. It defines sine law as relating each side of a triangle to the sine of its opposite angle. Sine law is used when the given data includes a side and its opposite angle. Cosine law defines the square of any side as the sum of the squares of the other two sides minus twice the product of those sides times the cosine of the angle between them. Cosine law can be used to solve for any side or angle of a triangle given the other two sides and their included angle.

2. •Oblique Triangles
•Sine Law
•Cosine Law
•Application of the Sine
and the Cosine Law

3. •Oblique Triangles
a. The Sum of the three angles is equal to 1800 .A
+ B + C = 1800;
b. The greater angles subtends the longer side, if
A> B > C, then a> b> c;
c. A triangle is determined or fixed in form and
in size if the following parts are given:
a. Two angles and the side opposite one of
them;
b. Two sides and the angle opposite one of
them;
c. Two sides and the included angle;
d. Two angles and the included side;
e. Three sides
A plane triangle, which does not
contain a right angle
Figure 1

4. SINE LAW
Each side of a triangle
is directly proportional to
the sine of the opposite angle.

5. Use the Sine Law
when there is a
“pair” in the
given data.
“Pair” means a side
and its opposite
angle. For example,
angle A and side a
constitutes a pair.
TIP

6. COSINE LAW
The square of any side of a triangle is equal to the
sum of the squares of the other two sides minus twice
the product of these two sides times the cosine of the
angle between these two sides.
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C

7. COSINE LAW
The square of any side of a triangle is equal to the
sum of the squares of the other two sides minus twice
the product of these two sides times the cosine of the
angle between these two sides.
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C