Final answer:
The length of side DE in triangle DEF can be calculated using the Law of Cosines, inserting the known lengths of sides EF and DF, and the 60-degree angle at F.
Step-by-step explanation:
To find the length of side DE in a triangle DEF, we will apply the Law of Cosines since we have two sides and the included angle. The Law of Cosines states that in any triangle, the length of a side squared is equal to the sum of the squares of the other two sides minus twice their product and the cosine of the included angle. For triangle DEF with sides EF, DF, and DE, and an angle F of 60 degrees, the formula is:
DE^2 = DF^2 + EF^2 - 2(DF)(EF)cos(F)
Plugging in the known values:
DE^2 = 7.9^2 + 4.2^2 - 2(7.9)(4.2)cos(60°)
By calculating this, we find the length of DE.