ANSWER NEEDED

A triangle has sides measuring 12 cm and 18 cm. The angle opposite the 12-cm side measures 28°. Which statement is TRUE given that all angle measurements are rounded to the nearest degree?

A

There are two possible values for the measure of the largest angle of the triangle, and 107° is the greatest.

B

There is only one possible value for the measure of the largest angle of the triangle, 107°.

C

There are two possible values for the measure of the largest angle of the triangle, and 135° is the greatest.

D

There is only one possible value for the measure of the largest angle of the triangle, 135°.

The diagram of the triangle is shown in the attached photo. Since the length of two sides and one angle is known, we will apply the sine rule. It states that

a/sin A = b/sin B = c/sin C

From the triangle

b = 12

c = 18

12/sin 28 = 18/sinC

Cross multiplying

12SinC = 18sin28

12SinC = 18×0.4695

12sinC = 8.451

SinC = 8.451/12 = 0.70425

C = Sin^-1(0.70425) = 44.77

Since the sum of the angles in a triangle is 180 degrees,

Angle A = 180 - 28 - 44.77 = 107

Therefore, the following statements are true

There is only one possible value for the measure of the largest angle of the triangle, 107°.