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never [62]
3 years ago
14

Someone please help me with this one quick

Mathematics
1 answer:
astraxan [27]3 years ago
4 0

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

<u>Let us first find angle C:</u>

<em>Sum of all angles in a triangle = 180°</em>

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°

<u>To find the length of AC:</u>

<em>Using sine formula:</em>

$\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.

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