Answer:
Angle C ∠C = 160.49°
side b = 0.522 m
side a = 17.34 m
Step-by-step explanation:
Given that;
In a Δ ABC,
∠A = 18.95°
∠B = 0.56°
∠C = ???
side A = ???
side B = ???
side C = 17.83 m
We are to determine the unknown missing sides and the angle.
We know that, the sum of angles in a triangle = 180°
∴
∠A + ∠B + ∠C = 180°
18.95° + 0.56° + ∠C = 180°
∠C = 180° - 18.95° - 0.56°
∠C = 160.49°
Using sine rule to determine the unknown sides. The sine rule can be expressed as:
[tex]\mathtt{\dfrac{sin \ A}{a} = \dfrac{sin \ B}{b} = \dfrac{sin \ C}{c} }[/tex]
To determine side b, we have:
[tex]\mathtt{ \dfrac{sin \ B}{b} = \dfrac{sin \ C}{c} }[/tex]
[tex]\mathtt{ \dfrac{sin \ 0.56^0}{b} = \dfrac{sin \ 160.49}{17.83} }[/tex]
[tex]\mathtt{ b (sin \ 160.49) = 17.83 (sin \ 0.56)}[/tex]
[tex]\mathtt{ b = \dfrac{17.83 (sin \ 0.56)}{(sin \ 160.49)}}[/tex]
[tex]\mathtt{ b = \dfrac{17.83 \times 0.0097737}{0.33397}}[/tex]
[tex]\mathtt{ b = \dfrac{0.174265071}{0.33397}}[/tex]
b = 0.522 m
For side a, we have
[tex]\mathtt{\dfrac{sin \ A}{a} = \dfrac{sin \ B}{b} }[/tex]
[tex]\mathtt{\dfrac{sin \ 18.95}{a} = \dfrac{sin \ 0.56}{0.522} }[/tex]
[tex]\mathtt{a \times sin \ 0.56 = 0.522 (sin \ 18.95)}[/tex]
[tex]\mathtt{a = \dfrac{0.522 (sin \ 18.95)}{ sin \ 0.56}}[/tex]
[tex]\mathtt{a = \dfrac{0.522\times 0.3247 }{ 0.0097737}}[/tex]
a = 17.34 m
