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Solve for the missing sidebof the triangle shown in the figure​

Solve for the missing sidebof the triangle shown in the figure​-example-1
User Plopp
by
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1 Answer

5 votes

Answer:

∠B = 74°

a ≈ 14.5 inches

c ≈ 11.4 inches

Explanation:

The given parameters of triangle ΔABC are;

∠A = 62.2°, ∠C = 43.8° and side
\overline{AB} = b = 15.8 in

By sine rule, we have;


(a)/(sin(\angle A)) = (b)/(sin(\angle B)) = (c)/(sin(\angle C))


a = {sin(\angle A)} * (b)/(sin(\angle B))

By angle sum property, we have;

∠B = 180° - (∠A + ∠C)

∴ ∠B = 180° - (62.2° + 43.8°) = 74°

∠B = 74°


\therefore {a} = {sin(62.2^(\circ))} * (15.8)/(sin(74^(\circ))) \approx 14.5

a ≈ 14.5 in.


c = {sin(\angle C)} * (b)/(sin(\angle B))


\therefore {c} = {sin(43.8^(\circ))} * (15.8)/(sin(74^(\circ))) \approx 11.4

c ≈ 11.4 in.

User Seekheart
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