Question #142866
Solve the following triangles. Identify the case # in each given
triangle.

4.) b= 4.2 c= 3.5 C= 51°48'
1
Expert's answer
2020-11-09T19:36:57-0500

b=4.2cmc=3.5cmC=51°48=51.8°b = 4.2cm\\ c = 3.5cm\\ C = 51°48' = 51.8°






To solve for angle B, we use the sine rule,

bsinB=csinC4.2sinB=3.5sin51.8sinB=4.2×sin51.83.5sinB=0.9430B=70.6°\begin{aligned} \dfrac{b}{sinB} &= \dfrac{c}{sinC}\\ \\ \dfrac{4.2}{sinB} &= \dfrac{3.5}{sin51.8}\\ \\ sinB &= \dfrac{4.2×sin51.8}{3.5}\\ \\ sinB &= 0.9430\\ B &= 70.6° \end{aligned}


To solve for angle A,

Sum of internal angles in a triangle = 180°

\therefore A + B + C = 180°

A = 180° - B - C

A = 180° - 70.6° - 51.8°

\therefore A = 57.6°


To solve for side a, we use the sine rule;

asinA=csinCasin57.6=3.5sin51.8a=3.5×sin57.6sin51.8a=3.76cm\begin{aligned} \dfrac{a}{sinA} &= \dfrac{c}{sinC}\\ \\ \dfrac{a}{sin57.6} &= \dfrac{3.5}{sin51.8}\\ \\ a &= \dfrac{3.5× sin57.6}{sin51.8}\\ \\ a &= 3.76cm \end{aligned}



\therefore a = 3.76cm, b = 4.2cm, c = 3.5cm

A = 57.6°, B = 70.6°, C= 51.8°


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