The solutions to this triangle are:
- 7.9
- 44.1 degrees
- 83.7 degrees
How to solve for the triangle
Using the law of cosine we would have
a²=b²+c²-2bc cos A
a² =100+49-2(10)(7)cos 52
This would give us
=149 -140 x (0.6157)
=62.82
We take the square root of 62.82 =
7.93 or 7.9
We have to use the sine law to find the other side
7.9/sin 52=10.057
10.06=7/sin C
such that
sin C = sin(0.6958)
=44.1°
10.06=10/sin B
cross multiply
sin B=10/10.06
= sin⁻¹0.9940
Then B = 83.7°
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