Solving SAS Triangles

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

SAS Triangle

How to solve an SAS triangle ?

  1. use the Law of Cosines to calculate the unknown side,
  2. use the Law of Sines to find the smaller of the other two angles,
  3. use the three angles add to 180° to find the last angle.

Example
Solving SAS Triangles

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

Learn More

Solving SSA Triangles

Solving SSS Triangles

Finding an Angle in a Right Angled Triangle

Angles of Elevation & Depression

Algebra Index

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