Question

Calculate the side lengths a and b to two decimal places.

Answer 1

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,

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

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,

$\frac{a}{\sin 50^{\circ}}= \frac{b}{\sin 107^{\circ}}=\frac{c}{\sin 23^{\circ}}$

Consider first and last  ratios, we have,

$\frac{a}{\sin 50^{\circ}}=\frac{c}{\sin 23^{\circ}}$

Solving for a, we have,

$a=\frac{\sin \left(50^{\circ \:}\right)}{\sin \left(23^{\circ \:}\right)}\cdot \:8$

We get , a = 15.68

Consider last two ratios, we have,

$\frac{b}{\sin 107^{\circ}}=\frac{c}{\sin 23^{\circ}}$

and now solving for b ,

$b=\frac{\sin \left(107^{\circ \:}\right)}{\sin \left(23^{\circ \:}\right)}\cdot \:8$

We get , b = 19.58

Thus, option (a) is correct.

a = 15.68 and  b = 19.58

Answer 2

Missing angle: 180 - 107 -50 = 23 degrees

a = a/ sin(50) = 8/sin(23)

a(sin(23) = 8sin(50)
a*0.3907 = 6.1284
a = 6.1284 / 0.3907 = 15.68

since there is only one answer that has that value for a

 the answer is A