Question

HOW TO DO THIS QUESTION ​

Answer 1

9514 1404 393

Answer:

64.2 cm²

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

__

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

A ≈ 40.3 cm²

Explanation:

The area of right Δ ACD is calculated as

A =
`(1)/(2)` bh ( b is the base and h the perpendicular height )

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

`(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 =
`(1)/(2)` × BC × AC × sin36°

= 0.5 × 19 × 7.214 × sin36°

≈ 40.3 cm² ( to 3 sf )