Find the area of triangle ABC if the area of triangle CDE is given as 20cm². C 12cm 25⁰ A 110⁰ D C 45⁰ CE 6cm 25⁰
In order to find the area of triangle ABC, we first need to find the length of side AB.
By applying the Law of Sines in triangle CDE, we can find the length of side CD:
CD/sin(25) = CE/sin(45)
CD = CE(sin(25))/sin(45) = 6(sin(25))/sin(45) = 6(0.42262)/(0.70711) = 3.571cm
Now, by applying the Law of Sines in triangle ABC, we can find the length of side AB:
AB/sin(25) = CD/sin(110)
AB = CD(sin(25))/sin(110) = 3.571(sin(25))/sin(110) = 3.571(0.42262)/(0.93969) = 1.6004cm
Now, we can find the area of triangle ABC using the formula for the area of a triangle:
Area = 1/2 * AB * CE * sin(25)
Area = 1/2 * 1.6004 * 6 * sin(25)
Area = 1.3519 cm²
Therefore, the area of triangle ABC is 1.3519 cm².