In triangle DEF, side E is 4 cm long and side F is 7 cm long. If the angle between sides E and F is 50 degrees, how long is side D?

In triangle DEF, side E is 4 cm long and side F is 7 cm long. If the angle between sides E and F is 50 degrees, how long is side D?

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Faiza Fuller

This is a SAS triangle (two sides and an included angle) so we can use the Law of Cosines to find the length of side D:

$$D^{2}=E^"{2}+F^{2}−2EF\cos\theta$$

$$D^{2}=4^{2}+7^{2}-2(4)(7)\cos50^{\circ}$$

$$D^{2}=65-56\cos50^{\circ}$$

$$D=\sqrt{65-56\cos50^{\circ}}$$

$$D \sim 5.4 cm$$