The Rules of Sine

A

B C

c b

a

How about for scalene triangle ?

C

A B

a

c

b

D

h

Height line is the line from an angle of triangle that is perpendicular with opposite side.

Look at the triangle beside!

By the same way, we get :

So, we get :

It is called by the rule of sine.

This rules can be used for cases :

• Two angles and any one side length are given

• Two sides and an angle of opposite side are given

A B

C

a b

c D

Example Determine the size of angle and the length of sides that are not given from the triangle below :

A C

B

5 cm

Answer

Activities Class

1. Determine the undetermined elements from triangle of KLM :

M

K 25 cm L

Given : the angle of K is 400 and the angle of L is 550.

2. Desi and Vita are standing on the edge of a river and are separated as far as 40 m. across the river, Ardi is seen to be standing and looking at both the girls. If the angle formed by Ardi-Desi-Vita is 650 and the angle formed by Ardi-Vita-Desi is 500. Determine the distance of Ardi and Desi and the distance of Ardi from Vita!