The two sides of the triangle are 49 cm and 99 cm, and the angle between them is 59 °

The two sides of the triangle are 49 cm and 99 cm, and the angle between them is 59 °. What is this triangle: a) acute-angled, b) rectangular, or c) obtuse?

1. Let in triangle ABC:

BC = a = 49 cm;
AC = b = 99 cm;
∠C = 59 °.
2. Find the third side of the triangle using the cosine theorem:

c ^ 2 = a ^ 2 – 2abcos∠C + b ^ 2;
c ^ 2 = 49 ^ 2 – 2 * 49 * 99cos59 ° + 99 ^ 2 = 2401 – 9702 * 0.5150 + 9801 = 12202 – 4996.8994 = 7205.1006;
c = 84.88 (cm).
3. Apply the cosine theorem again:

b ^ 2 = a ^ 2 – 2accos∠B + c ^ 2;
cos∠B = (a ^ 2 + c ^ 2 – b ^ 2) / (2ac);
a ^ 2 + c ^ 2 – b ^ 2 = 49 ^ 2 + 84.88 ^ 2 – 99 ^ 2 = -195.3856 <0;
cos∠B <0, then:
∠B> 90 ° – blunt.
Answer: obtuse.