SOLUTION: If a given triangle ABC with a = 12, b = 10 and c = 8, please help me find the angles in minutes. angle A = ___________ _ angle B = ___________ _ angle C = ___________ _

Algebra ->  Trigonometry-basics -> SOLUTION: If a given triangle ABC with a = 12, b = 10 and c = 8, please help me find the angles in minutes. angle A = ___________ _ angle B = ___________ _ angle C = ___________ _      Log On


   

Question 93616This question is from textbook
: If a given triangle ABC with a = 12, b = 10 and c = 8, please help me find the angles in minutes.
angle A = _____________
angle B = _____________
angle C = _____________ This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If a given triangle ABC with a = 12, b = 10 and c = 8, please help me find the angles in minutes.
:
Using the law of cosines: a^2 = b^2 + c^2 - 2bc*Cos(A)
:
Rearrange formula to find Angle A
Cos(A) = %28b%5E2+%2B+c%5E2+-+a%5E2%29%2F%282bc%29
:
Cos(A) = %2810%5E2+%2B+8%5E2+-+12%5E2%29%2F%282%2A10%2A8%29
:
Cos(A) = %28100+%2B+64+-+144%29%2F%28160%29 = 20%2F160 = .125
:
A = 82.81924422 degrees
Find the minutes, mult the decimal portion times 60:
A = 82 degree, 49.15 minutes
:
:
Find Angle B
Cos(B) = %28a%5E2+%2B+c%5E2+-+b%5E2%29%2F%282ca%29
:
Cos(B) = %2812%5E2+%2B+8%5E2+-+10%5E2%29%2F%282%2A8%2A12%29
:
Cos(B) = %28144+%2B+64+-+100%29%2F%28192%29 = 108%2F192 = .5625
:
B = 55.77113367 degrees
Find the minutes, mult the decimal portion times 60:
B = 55 degrees, 46.28 minutes
:
:
Find Angle C by subtracting the known angles from 180:
:
180 - 82.81924422 - 55.77113367 = 41.40962211
Which is:
C = 41 degrees, 24.58 minutes
:
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