Question

Which parts of △DEF can be determined using only the Law of Cosines?Drag each statement into the correct box.

Answer 1

The Law of Cosines

Given a triangle DEF where two side lengths DF and EF are given and their included angle F, the third side DE can be calculated by:

`DE^2=DF^2+EF^2-2DF\cdot DE\cos F`

As seen the side length DE can be calculated by using the law of cosines.

Once we have the value of this side length, we can calculate the other two angles by using either the law of sines or the law of cosines, but DE can only be calculated by the use of the law of cosines.

Answer: If no other part has been calculated before, DE can only be determined by using the law of cosines.