Download Trigonometry in Non-Right Angled Triangles Area of a Triangle Sine

Trigonometry in Non-Right Angled Triangles
Area of a Triangle
You need to know 2 sides and the angle in between.
Example:- Calculate the area of this triangle.
Area = ½ ab Sin C
= ½ x 16 x 16 x Sin 35o
= 73.4177…
= 73.4 cm2
Sine Rule
Look for pairs of angles and sides. Need to know one pair (angle and side) plus
angle/side opposite required side/angle.
Example:- Find the length of the missing side, x cm.
Example:- Find the size of the missing angle, xo.
Always to 3 decimal places!!
Remember to use SHIFT SIN
=>
𝑥 = 𝑠𝑖𝑛−1 0.945 = 70.8𝑜 .
Cosine Rule
To find a missing side
To find a missing angle
Use the Cosine rule when you are involving all three sides of the triangle.

For a side – you know 2 sides (with the angle in between) and want to know the
3rd side.

For an angle – you know all 3 sides to start with.
Example :– Find the length of side BC.
a2 = b2 + c2 – 2bcCosA
= 62 + 92 – 2 x 6 x 9 x Cos32
= 36 + 81 – 91.589 = 25.411
a = √25.411 = 5.04m
So BC = 5.04m
Example :- Find the size of angle A.
Cos A =
𝑏2 + 𝑐 2 − 𝑎2
2𝑏𝑐
=
52 + 62 − 42
2 ×5 ×6
45
= 60 = 0.75
A = Cos-1 0.75 = 41.4o
=
25+36−16
60