Example 3

Determine the length of BD.

There is not enough information to determine BD using only \(\triangle\)BCD. Some information will need to come from \(\triangle\)ABC.

∠ACB and ∠BCD form a straight line, so their sum is 180°.

∠ABC can be determined using the sum of the interior angles in a triangle.

Knowing ∠ABC makes it possible to determine length BC using the sine law.

There is now enough information to determine BD using the sine law.

For further information about the sine law please see pp. 134–137 of Principles of Mathematics 11.

The sine law is a relationship between angle-side pairs in a triangle. It is often written as or . You can use the sine law to determine both unknown sides and unknown angles in a triangle. In the next lesson you will explore a relationship that uses the cosine ratio to solve for unknowns in any type of triangle.