## Solving SAS Triangles

SAS (Side, Angle, Side) is when we know 2 sides and the angle between them.

Table of Contents

## 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:**

*b*^{2}* ** **= a*^{2 }*+ c*^{2}* − 2ac cos B*

= (2.6)^{2} + (6.9)^{2 }– 2 × 6.9 × 2.6 × cos 117^{o}

= 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