The lengths of the triangle shown below are rounded to the nearest 0.1 cm. What is the area, to the nearest 1 cm2, of this triangle?
(Note: The area of any triangle with sides of length a, b, and c opposite angles of measure A, B, and C, respectively, is given by 1/2 ab sin C.)
The correct answer is C.
Area of the triangle = 1/2 ab sin C
Since only one angle measure is given in the triangle, use that for C in the formula.
Area = 1/2 ab sin 30°
The length of the side opposite from angle C, the 30° angle, is 5.0 cm and must correspond to side c. That means that the other side lengths, 8.0 cm and 4.0 cm, correspond to sides a and b.
So, area = 1/2 x (8.0) x (4.0) x sin 30°
Since, sine 30° = 1/2
Area = 8 cm2