Page 49 - modul trigonometri_Neat

D. Sinus Rules, Cosine Rules, and Triangle Area

In the ABC triangle with side lengths a, b and c apply the rules of
the sinuses, cosine and the area of the triangle.

1. Sinus Rules

= =
sin sin sin

2. Cosine Rules

2
2
2
= + − 2 cos
2
2
2
= + − 2 cos
2
2
2
= + − 2 cos

3. Triangle Area
a. Broad Triangle that Known Two Side and One Corner
1
Broad ∆ = × sin
2
1
Broad ∆ = × sin
2
1
Broad ∆ = × sin
2

b. The Area of a Known Triangle Of Two Angles and One Side

× sin × sin
2
Broad ∆ = 2 sin
2
Broad ∆ = × sin × sin
2 2 sin
Broad ∆ = × sin × sin
2

c. The Area of the Triangle Known to Be The Length of The Three
Sides

Broad ∆ = √ ( − )( − )( − )
1
with s = ( + + ) = half the circumference of the ABC triangle
2

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