Question

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

Answer 1

Answer:

Length of side AB = 10.2m

Step-by-step explanation:

Given:

The given area of triangle ADC = 52m²

Side AD = 12m,

Given angle D = 102°

Then we can calculate the area of triangle ADC using below formula

Area= ½ × a × b × sin(C)

52m² = ½ × 12 × CD × sin102

But sin102= 0.9781

52 = 6 × CD *(0.9781)

CD = 52/(6× 0.9781)

CD = 52/5.8686

Therefore, the length of side CD= 8.86m= 8.9m If we approximate

If we will need to find sides AC by applying Cosine rule as follows

d² = a² + c² -2ad ×(cosD)

d² = 8.9² + 12² - 2*8.9*12× Cos102

Cos102 = -0.2079

d² = 267.61744

d = √267.61744

Therefore, sides AC = 16.4m

We can apply sine rule to ∆ABC as

xsinX = y/sinBY

AB/sin46) = AC/(sin120)

AB/0.7193 = 16.4/(0.866)

AB = (14.2023) ×0.7193

Therefore, side AB = 10.2m