Calculate the side lengths a and b to two decimal places

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Step-by-step explanation:

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,

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,

Consider first and last  ratios, we have,

Solving for a, we have,

We get , a = 15.68

Consider last two ratios, we have,

and now solving for b ,

We get , b = 19.58

Thus, option (a) is correct.

a = 15.68 and  b = 19.58