Calculate the area of the shaded region. Show ALL of your work
2 answers:
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BC is 10 units and AC is units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵
∵ AB =
- Substitute AB and the 3 angles in the rule above
∴
- By using cross multiplication
∴ (BC) × sin(30) = × sin(45)
∵ sin(30) = 0.5 and sin(45) =
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵
- Substitute AB and the 3 angles in the rule above
∴
- By using cross multiplication
∴ (AC) × sin(30) = × sin(105)
∵ sin(105) =
∴ 0.5 (AC) =
- Divide both sides by 0.5
∴ AC = units
BC is 10 units and AC is units
Learn more:
You can learn more about the sine rule in brainly.com/question/12985572
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