Question

There may be several triangles ABC with b=122, c=169, angle B=40 degrees. Find dimensions for the one with the largest value of a

Answer 1

Explanation:

Using sine rule:

sin 40 / 122 = sin c / 169

169 sin 40 / 122 =sin C

C= 62.9°

then A = 180 - 62.9 -40 = 77.1 °

Use sin rule again to find 'a'

sin40 /122 = sin A /a

a = sin A / ( sin40 / 122) = 185 units

As a partial check:

Using triangle side length rule

169 + 122 > a

291>a so the biggest integer 'a' would be at most 290 units