Find the missing length of side b. Area =28.19in, <C =110°,a = 6in

Question

Find the missing length of side b. Area =28.19in, <C =110°,a = 6in

Answer 1

Use the Area Formula for a non-right Triangle: A = ¹/₂ a.b.sinC

28.19 = ¹/₂ (6)b.sin110°

b = 28.19/(3sin110°) = 10.0 inches

Answer 2

area = 28.19 square inches

side a = 6 inches

height of the triangle is 2(28.19/6) = 4.698666...= about 9.4

angle C = 110 degrees

construct a right triangle adjoining, to the left of the given triangle, with b = hypotenuse, 9.4 = height, angle opposite b = 180-110 = 70 degrees sin90 = 1

use the Law of Sines

b/sin90 = 9.4/sin70

b/1 = 9.4/sin70

b = 9.4/sin70 = 9.4/.94 = 10 inches