# Applications of the sine law and cosine law

### Applications of the sine law and cosine law

What's the purpose of learning the Law of Sines and the Law of Cosines? To solve real-life problems! In this section on applications of the two laws, we will apply our trigonometry knowledge to tackle distance problems.
Basic concepts: Law of sines, Law of cosines,

#### Lessons

• 1.
Neo left home and drove to a grocery store on a bearing of N15°W. Then he drove to a mall located 11km away from the grocery store. If the mall is 13 km away on a bearing of N60°W from his home, what is the distance between Neo's home and the grocery store?

• 2.
Owen sees a firework on a bearing of 290°. Meanwhile 6km due west of Owen, Macy sees the same firework on a bearing of 065°.
a)
How far is each person away from the firework?

b)
If Macy's parents are enjoying the firework 1.5 km due north of Macy, how far are Macy's parents from the firework?