Question

Given Triangle ABC: I think there are suppose to be right triangles...

1) If <A = 30º, and c = 20, find a, b, and <B
2) If a = 10 and b = 14, find c, <A, and <B
3) If a = 6 and <B = 53º, find b, c, and <A
4) If c = 13 and b = 12, find a, <A, and <B
5) If <A = 20º and b = 10, find <B, a and c
6) If c = 30 and <A = 40º, find <B, a, and b

Answer 1

I'm assuming all rt triangles.

1. Given: A = 30, c = 20.

a = csinA = 20sin30 = 10,
b = ccosA = 20cos30 = 17.3,
B = 90 - A = 90 - 30 = 60.

2. Given: a = 10, b = 14.

c^2 = a^2 + b^2 = 10^2 + 14^2 = 100 + 196 = 296,
c = sqrt(296) = 17.2
tanA = a/b = 10/14 = 0.7143, A = 35.5,
B = 90 - A = 90 - 35.5 = 54.5.

The remaining problems are similar.