ABC and ADC are triangles. The area of triangle ADC is 52m^2. Work out the length of AB. Give your answer to 1 decimal place.

AB = 10.2m

Step-by-step explanation:

Area of triangle ADC = 52m²

AD = 12m, angle D = 102°

Area of triangle ADC = ½ × a × b × sinC

52m² = ½ × 12 × CD × sin102

52 = 6 × CD × 0.9781

CD = 52/(6× 0.9781)

CD = 52/(5.8686)

CD = 8.86m = 8.9m (1 decimal place)

Using Cosine rule to find AC = d

d² = a² + c² -2×a×d ×cosD

d² = 8.9² + 12² - 2×8.9×12× Cos102

Cos102 = -0.2079

d² = 267.61744

d = √(267.61744)

AC = d = 16.4m

For ∆ABC

Using sine rule:

a/sinA = b/sinB

AB/sin46 = AC/sin120

AB/0.7193 = 16.4/0.866

AB = 14.2024 ×0.7193

AB = 10.2m (1 decimal place)

13.6

Step-by-step explanation:

See photo

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