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:

`$(b)/(\sin B ) =(c)/(\sin C)`

Substitute the given values in the formula.

`$(b)/(\sin 89^\circ ) =(14)/(\sin 61^\circ )`

Multiply by sin 89° on both sides.

`$\sin 89^\circ * (b)/(\sin 89^\circ ) =(14)/(\sin 61^\circ ) * \sin 89^\circ`

`$b=(14)/(0.8746 ) *0.9998`

`b=16`

The length of AC is 16 km.