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Ответ:

anayamulay

11.03.2020

Mathematics

∠B = 74°

a ≈ 14.5 inches

c ≈ 11.4 inches

Step-by-step 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;

$\dfrac{a}{sin(\angle A)} = \dfrac{b}{sin(\angle B)} = \dfrac{c}{sin(\angle C)}$

$a = {sin(\angle A)} \times \dfrac{b}{sin(\angle B)}$

By angle sum property, we have;

∠B = 180° - (∠A + ∠C)

∴ ∠B = 180° - (62.2° + 43.8°) = 74°

∠B = 74°

$\therefore {a} = {sin(62.2^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 14.5$

a ≈ 14.5 in.

$c = {sin(\angle C)} \times \dfrac{b}{sin(\angle B)}$

$\therefore {c} = {sin(43.8^{\circ})} \times \dfrac{15.8}{sin(74^{\circ})} \approx 11.4$

c ≈ 11.4 in.

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