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
