Answer to Question #142866 in Trigonometry for Raffy

Question

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

4.) b= 4.2 c= 3.5 C= 51°48'

Answer 1

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

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

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

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;

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

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

A = 57.6°, B = 70.6°, C= 51.8°