Asked by Mike
Find the indicated angle è.
(Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 110 and c = 136 (angle B=38)
Round your answer to two decimal places.)
(Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 110 and c = 136 (angle B=38)
Round your answer to two decimal places.)
Answers
Answered by
Henry
Law of Cosines:
cosB = (a^2+c^2-b^2)/2ac.
cos38 = ((110)^2+(136)^2-b^2) / 29920.
0.7880 = (30596-b^2) / 29920.
Cross multiply:
30,596-b^2 = 0.7880*29920 = 23576.96.
-b^2 = 23,976.96-30596 = -6619.04.
b^2 = 6619.04.
b = 81.36.
Law of Sines:
sinA/a = sinB/b.
sinA / 110 = sin38 / 81.36.
Multiply both sides by 110:
sinA = 110(sin38 / 81.36) = 0.832384.
A = 56.34 Deg.
C = 180 - 38 - 56.34 = 85.66 Deg.
cosB = (a^2+c^2-b^2)/2ac.
cos38 = ((110)^2+(136)^2-b^2) / 29920.
0.7880 = (30596-b^2) / 29920.
Cross multiply:
30,596-b^2 = 0.7880*29920 = 23576.96.
-b^2 = 23,976.96-30596 = -6619.04.
b^2 = 6619.04.
b = 81.36.
Law of Sines:
sinA/a = sinB/b.
sinA / 110 = sin38 / 81.36.
Multiply both sides by 110:
sinA = 110(sin38 / 81.36) = 0.832384.
A = 56.34 Deg.
C = 180 - 38 - 56.34 = 85.66 Deg.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.