The unknown measurements of the triangle are C = 28°, c = 3.76 and b = 7.06.
Sine rule
Sine rule is used to show the relationship between sides of a triangle and the angles. It is given by:
- [tex]\frac{a}{sinA}= \frac{b}{sinB}=\frac{c}{sinC}[/tex]
Where a, b, c are the sides and the angles opposite the sides are A, B, C respectively.
- A + B + C = 180° (angles in a triangle)
- 62 + 90 + C = 180
- C = 28°
[tex]\frac{a}{sinA}= \frac{b}{sinB}\\
\\
\frac{8}{sin(90)}=\frac{b}{sin(62) }\\
\\
b=7.06\\
\\
\\
\frac{a}{sinA}= \frac{c}{sinC}\\
\\
\frac{8}{sin(90)}=\frac{c}{sin(28) }\\
\\
c=3.76[/tex]
The unknown measurements of the triangle are C = 28°, c = 3.76 and b = 7.06.
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