Question

Solve the triangle (Use Law of Sines) A = 30°, a = 13, b = 26

Answer 1

You can set up the equation like this:

(sin 30°) / 13 = (sin B) / 26

Now, you can solve for sin B:

sin B = (sin 30° * 26) / 13
sin B = (1/2 * 26) / 13
sin B = 13 / 13
sin B = 1

Now, to find angle B, take the arcsin (inverse sine) of 1:

B = arcsin(1)
B = 90°

Now that you have angle B, you can find angle C using the fact that the sum of angles in a triangle is 180°:

C = 180° - A - B
C = 180° - 30° - 90°
C = 60°

So, the solution to the triangle is:
A = 30°
B = 90°
C = 60°
a = 13
b = 26