Here is the sketch of the triangle;
We are given all the three sides. We need to calculate the three angles A, B, and C.
Here we apply cosine rule.
a2=b2+c2−2bccosA
And this can be re-written as;
cosA=2bcb2+c2−a2
cosA=2×267×4122672+4122−1732
=22000871289+169744−29929
=220008211104
=0.95952874441
∴cosA=0.95952874441
A=cos−1(0.95952874441)
=16.36°
To find angle B, we again apply cosine rule
b2=a2+c2−2accosB
Which can also be re-written;
cosB=2aca2+c2−b2
cosB=2×173×4121732+4122−2672
=14255229929+169744−71289
=142552128384
=0.90061170661
B=cos−1(0.90061170661)
B=25.76°
To find the final angle C, we apply the property: 'The sum of the three interior angles of a triangle add up to 180°'
∴C=180°−(A+B)
=180°−(16.36°+25.76°)
=180°−42.12°
=137.88°
Therefore, the three angles are;
A=16.36°
B=25.76°
C=137.88°
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