Answer:
A = 36.9°
Explanation:
In this triangle we know the three sides:
AB = 3,
BC = 4 and
CA = 5.
Use The Law of Cosines first to find angle A first:
cos A = (BC² + CA² − AB²) / 2BCCA
cos A = (4² + 5² − 3²) / (2×4×5)
cos A = (16 + 25 − 9) / 40
cos A = 0.80
A = cos⁻¹(0.80)
A = 36.86989765°
A = 36.9° to one decimal place.
Next we will find another side. We use The Law of Cosines again, this time for angle B:
cos B = (CA² + AB² − BC²) / 2CAAB
cos B = (5² + 3² − 4²) / (2×5×3)
cos B = (25 + 9 − 16) / 30
cos B = 0.60
B = cos⁻¹(0.60)
B = 53.13010235°
B = 53.1° to one decimal place
Finally, we can find angle C by using 'angles of a triangle add to 180°:
C = 180° − 36.86989765° − 53.13010235°
C = 90°
Now we have completely solved the triangle i.e. we have found all its angles.
So we can analyze from above that the smallest angle in the triangle ABC is A with 36.9°.