Question

HOW TO DO THIS QUESTION ​

Answer 1

9514 1404 393

Answer:

  64.2 cm²

Step-by-step explanation:

The length AC is found from ...

  Area of ACD = (1/2)(AC)(CD)

  80.5 cm² = (1/2)(AC)(14 cm)

  AC = 80.5 cm²/(7 cm) ≈ 11.5 cm

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The area of ∆ABC is ...

  Area ABC = (1/2)(CB)(CA)sin(C)

  = (1/2)(19 cm)(11.5 cm)sin(36°) ≈ 64.2 cm²

Answer 2

Answer:

A ≈ 40.3 cm²

Step-by-step explanation:

The area of right Δ ACD is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height )

Here A = 50.5, b = CD and h = AC , then

$\frac{1}{2}$ × 14 × AC = 50.5

7 AC = 50.5 ( divide both sides by 7 )

AC ≈ 7.214

The area of Δ ABC is calculated as

A = $\frac{1}{2}$ × BC × AC × sin36°

  = 0.5 × 19 × 7.214 × sin36°

  ≈ 40.3 cm² ( to 3 sf )