Question

Determine the remaining sides and angles of the triangle ABC.

Answer 1

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:

$\mathtt{\dfrac{sin \ A}{a} = \dfrac{sin \ B}{b} = \dfrac{sin \ C}{c} }$

To determine side b, we have:

$\mathtt{ \dfrac{sin \ B}{b} = \dfrac{sin \ C}{c} }$

$\mathtt{ \dfrac{sin \ 0.56^0}{b} = \dfrac{sin \ 160.49}{17.83} }$

$\mathtt{ b (sin \ 160.49) = 17.83 (sin \ 0.56)}$

$\mathtt{ b = \dfrac{17.83 (sin \ 0.56)}{(sin \ 160.49)}}$

$\mathtt{ b = \dfrac{17.83 \times 0.0097737}{0.33397}}$

$\mathtt{ b = \dfrac{0.174265071}{0.33397}}$

b  = 0.522  m

For side a, we have

$\mathtt{\dfrac{sin \ A}{a} = \dfrac{sin \ B}{b} }$

$\mathtt{\dfrac{sin \ 18.95}{a} = \dfrac{sin \ 0.56}{0.522} }$

$\mathtt{a \times sin \ 0.56 = 0.522 (sin \ 18.95)}$

$\mathtt{a = \dfrac{0.522 (sin \ 18.95)}{ sin \ 0.56}}$

$\mathtt{a = \dfrac{0.522\times 0.3247 }{ 0.0097737}}$

a = 17.34 m