SOLUTION: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) b = 69, c = 35, ∠A = 72°

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Question 1191140: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.)
b = 69, c = 35, ∠A = 72°
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
Drawing and labeling your description, you will find that angle at point A is between the two sides of length b( 69 units) and c (35 units). You can use Law Of Cosines, and then any other skills and properties that you can identify.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i get:

angle A = 72 degrees.
a = 67.0

angle B = 78.2 degrees
b = 69

angle C = 29.8 degrees
c = 35

the sum of the angles is 180 degrees, as it should be.

the ratio of a / sine(A) = b / sine(B) = c/sine(C) is the same for all 3, as it should be.
that ratio was 70.482862 for all three.

the first thing i did was find the value of a using the law of cosines formula of:
a^2 = b^2 + c^2 - 2*a*b*cos(A).
the formula became:
a^2 = 69^2 + 35^2 - 2*69*35*cos(72) = 4493.447917
a = sqrt(4493.447917) = 67.03318519

once i got that, i was able to get the other values using the law of sines formula of:
a/sin(A) = b/sin(B) = c/sin(C)

a = 67.03318519
A = 72 degrees.

i got:
b = 69
B = 78.22636413 degrees.

and i got:
c = 35
C = 29.77363587 degrees.









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