Question

Someone please help me with this one quick

Answer 1

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

Let us first find angle C:

Sum of all angles in a triangle = 180°

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

To find the length of AC:

Using sine formula:

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

Substitute the given values in the formula.

$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }$

Multiply by sin 89° on both sides.

$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ$

$b=\frac{14}{0.8746 } \times0.9998$

$b=16$

The length of AC is 16 km.