Question

Can the measurement from △DEF be determined using only the Law of Cosines? State whether each measurement can be determined using only the Law of Cosines by answering “yes” or “no”.

m∠D =


m∠E =


DE =

Answer 1

9514 1404 393

Answer:

• ∠D - no
• ∠E - no
• DE - yes

Explanation:

With a single application of the Law of Cosines, you can only find one of an unknown side or an unknown angle. The other three elements in the 4-variable equation must be specified.

However, a single application of the LoC can be used to find DE. Then, knowing the three sides, either of the unknown angles can be found from an additional application of the LoC.

So, the answer is "it depends." It is yes to all if finding DE first is allowed. It is "no" to the angles if they must be found without finding DE first.