Hello! This week I will be covering the sine law in the trigonometry unit. The sin law is a very useful tool for solving triangles.
The sine law works for every triangle and the equation for it is: .
This means that when side a is divided by the sine of angle A, it is equal to the side b divided by the sine of angle B, which is equal to the side c divided by the sine of angle C.
Say you had to calculate side c.
Recall the law of sines. . First put in the values that we know:
. Ignore
as it does not have values that are useful to us.
Cross multiply to rearrange the equation and solve for side c.
We should have the answer of c = 11.8.
Say you had to calculate angle B.
Rearrange the law of sines to get . First put in the values that we know:
. Ignore
as it does not have values that are useful to us.
Like before, cross multiply to rearrange the equation and solve for angle C.
Use inverse sine to get rid of sin B = 0.7614… and isolate the variable B.
Our answer should be B = 49.6.
Hope this helps!