Find the missing side length BM. Round your answer to the nearest tenth.

Length of side BM is 30 yd

Step-by-step explanation:

⇒ ∠B + ∠M + ∠S = 180°

⇒ 35° + 102° + ∠S = 180°

∴ ∠S = 180° - 137° = 43°

Law of sines ⇒ a/sin A = b/sin B = c/sin C

Here, let BM be a then, sin A = sin S = sin 43° = -0.83

Also, b = 18 yd, then sin B = sin 35° = -0.43

⇒ BM/-0.83 = 18/-0.43

⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)

Step-by-step explanation:

Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°

Therefore, applying the rule,it becomes

18/Sin35 = BM/Sin43

Cross multiplying, it becomes

BM × Sin 35 = 18 × Sin 43

BM × 0.5736 = 18 × 0.6820

0.5736BM = 12.276

Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes

0.5736BM/0.5736 = 12.276/0.5736

BM = 21.4