# In triangle ABC, sin A = 0.3, sin B = 0.8, and b = 12. Find the length of side a.

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Given that :

sinA = 0.3

cosB = 0.8

Then we conclude that the angle C= 60 degree.

Then the hypotenuse is AB

But we know that sinA = opposite / hypotenuse= BC/AB

==> BC/AB = 0.3 ......(1)

sinB = AC/AB = 0.8 ............(2)

==> BC = 0.3 *AB

==> AC = 0.8*AB

==> 12 = 0.8 AB

Given that the sides b (AB) is 12.

==> AB= 12/.8 = 15

==> BC = 0.3 * 15 = 4.5

**Then the sides a is 4.5**

The sine rule of a triangle is a/ sin A= a/sinA = c/sin C.

a/0.3= 12/0.8 = C/sinC.

=> a = 0.3*12/0.8 =4.5

**So a = 4.5 units.**