how do i solve this

Question

Solve the triangle ABC if 

    

    degrees

    degrees

Assume  is opposite side ,  is opposite side , and  is opposite side .

Answer 1

I'd recommend the sine rule:

^{sin A} / _a = ^{sin B} / _b = ^{sin C} / _c

substitute the given values for b and c:

^{sin (40 deg)} / ₁₂₀ = ^{sin C} / ₁₆₇

=> sin C = ^{167 sin (40 deg)} / ₁₂₀

=> <C = arcsin ( ^{167 sin (40 deg)} / ₁₂₀ ) = 63.45° (or 63° to nearest °)

if <C = 63.45° and <B = 40° then <A = 180 - 40 - 63.45 = 76.55° (or 77° to nearest °)

so now ^{sin (40 deg)} / ₁₂₀ = ^{sin (76.55 deg)} / _a

=> ^{a sin (40 deg)} / ₁₂₀ = ^{sin (76.55 deg)}

=> a = ^{120 sin (76.55 deg)} / _{sin (40 deg)} = 181.57 (2 dp)