Suppose that A=103°, B=47°, and c=67. Solve the triangle round your answers to the nearest tenth

Answer 1

The interior angles of a triangle sum to 180°, so angle C must be 30°. Now use the Law of Sines:

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

You know sin(C) = sin(30°) = 1/2 and side c = 67, so sin(C)/c = (1/2)/67 = 1/134. Solving for a:

sin(A)/a = sin(C)/c

sin(103°)/a = 1/134

134·sin(103°) = a

Use your calculator to compute sin(103°) and get the answer. Do the same thing for sin(B)/b to solve for b. Then you will have solved the triangle because you have all three angle measures and all three side lengths.

Answer 2

103 + 47 + C = 180

C = 180-103-47 = 30 degrees for angle C

sinA/a = sinC/c = sin30/67 = 1/2/67 = 1/134

sin103/a = 1/134

a = 134sin103 = .9744(134) =130.6 for side a

sin47/b = 1/134

b = 134sin47 = 98.0 for side b

sides a, b, c are 130.6, 98.0 and 67

angles A, B, C are 103, 47, and 30 degrees

a is the side opposite angle A

b is the side opposite angle B

c is the side opposite angle C

the larger the angle the larger the side opposite the angle