Answer:
Area = 34.2 cm²
Explanation:
The general formula of the area of the triangle is half the product of two sides multiplied by the sine the angle between them.
So, for the given triangle ABC
AC = 9 cm, AB = 8 cm, CB = 10 cm
Area = 0.5 AC * AB * sin A or 0.5 BC * BA * sin B or = 0.5 CA * CB * sin C
Using the first form, so we need the measure of angle A
Using cosine low: cos A = (b² + c² - a²)/(2bc)
Where: a = BC = 10 , b = AC = 9 and c = AB = 8
So. cos A = (9² + 8² - 10²)/(2 * 9 * 8 ) = 0.3125
∠A = cos⁻¹0.3125 = 71.79°
So, Area = 0.5 AC * AB * sin A = 0.5 * 9 * 8 * sin 71.79° = 34.2 cm²
So, Area = 34.2 cm² to the nearest one decimal place