Answer:
Option (a) is correct.
a = 15.68 and b = 19.58
Step-by-step explanation:
Given: A triangle with some given measurements.
We have to find the values of a and b.
For a triangle ABC , with side opposite to angle A is a , side opposite to angle B is b and side opposite to angle C is c,
Using Sine rule , we have,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
For the given Δ ABC,
∠A = 50° , ∠B = 107°
AB = c = 8 , AC = b and BC = a
Using angle sum property of triangle,
Sum of angles of a triangle is always 180°
So , ∠A + ∠B +∠C = 180°
Solving for ∠C , we get,
∠C = 180° - 107° - 50°
∠C = 23°
Substitute in Sine rule , we have,
[tex]\frac{a}{\sin 50^{\circ}}= \frac{b}{\sin 107^{\circ}}=\frac{c}{\sin 23^{\circ}}[/tex]
Consider first and last ratios, we have,
[tex]\frac{a}{\sin 50^{\circ}}=\frac{c}{\sin 23^{\circ}}[/tex]
Solving for a, we have,
[tex]a=\frac{\sin \left(50^{\circ \:}\right)}{\sin \left(23^{\circ \:}\right)}\cdot \:8[/tex]
We get , a = 15.68
Consider last two ratios, we have,
[tex]\frac{b}{\sin 107^{\circ}}=\frac{c}{\sin 23^{\circ}}[/tex]
and now solving for b ,
[tex]b=\frac{\sin \left(107^{\circ \:}\right)}{\sin \left(23^{\circ \:}\right)}\cdot \:8[/tex]
We get , b = 19.58
Thus, option (a) is correct.
a = 15.68 and b = 19.58
