Question

Could anyone please walk me through the necessary steps for this?
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Answer 1

Answer: m∠C=45° AB=12.4 units AC=15.9 units

Explanation:

Given: m∠A=20° m∠B=115° BC=6 units

Find: 1) m∠C=? 2) AB=? AC=?

1)

m∠C=180°-(m∠A+m∠B)

m∠C=180°-(20°+115°)

m∠C=180°-135°

m∠C=45°

2)

We use the sine theorem to find the length of a side of a triangle:

`\displaystyle\\a)\ (BC)/(sin20^0) =(AB)/(sin45^0) \\\\AB=(BCsin45^0)/(sin20^0)\\\\AB=(6*0.707)/(0.342) \\\\AB\approx12.4 \ units\\`

`\displaystyle\\b )\ (BC)/(sin20^0) =(AC)/(sin115^0)\\\\AC=(BCsin115^0)/(sin20^0) \\\\AC=(6*0.906)/(0.342) \\\\AC\approx15.9\ units`