Answer:
Step-by-step explanation:
Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,
Tan BEC = 6/3 = 2
Angle BEC = Tan^-1(2)
Angle BEC = 63.4°
The sum of the angles on a straight line is 180°. This means that
Angle AED + angle DEC + angle BEC = 180
Angle AED = 180 - (45 + 63.4) = 71.6°
Angle ADE = angle AED = 71.6°
Angle CDE + angle ADE = 180(sum of angles on a straight line)
Angle CDE = 180 - 71.6 = 108.4°
To get line EC, we would apply Pythagoras theorem. Therefore
EC² = 3² + 6² = 45
EC = √45 = 6.71 cm
The sum of the angles in a triangle is 180°
Therefore,
Angle ECD = 180 - (45 + 108.4) = 26.6°
By applying sine rule,
6.71/sin108.4 = ED/sin26.6 = DC/Sin45
6.71/sin108.4 = ED/sin26.6
Cross multiplying, it becomes
6.71sin26.6 = EDsin108.4
ED = 6.71sin26.6/sin108.4
ED = 3.00608/0.949 = 3.18cm
The area of a triangle is
Area = 1/2abSinC
Therefore, area of triangle EDC = 1/2 ×
ED × EC × SinDEC
Area = 1/2 × 6.71 × 3.18 × sin45
Area = 1/2 × 6.71 × 3.18 × 0.707
Area = 7.54 cm²
