SAS (Side, Angle, Side) is when we know 2 sides and the angle between them.
How to solve an SAS triangle ?
- use the Law of Cosines to calculate the unknown side,
- use the Law of Sines to find the smaller of the other two angles,
- use the three angles add to 180° to find the last angle.
Example
Step 1:
b2 = a2 + c2 − 2ac cos B
= (2.6)2 + (6.9)2 – 2 × 6.9 × 2.6 × cos 117o
= 47.61 + 6.76 − 35.88 × (−0.4539…)
= 70.659…
b = √70.659…
= 8.405…
= 8.41 (to 2 decimal places)
Step 2:
sin C / c = sin B / b
sin C / 6.9 = sin(117°) / 8.405…
sin C = (6.9 × sin(117°)) / 8.405…
sin C = 0.7313…
C = sin−1(0.7313…)
C = 47.0° (to 1 decimal place)
Step 3:
A = 180° − 117° − 47.0°
A = 16.0° to one decimal place