In Triangle DEF, if e=8, f=3, and cosD=3/4, how do you find the exact value of d?

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Answer 1 · 2017-04-29T08:44:12

Using the Law of Cosines we get: #d=sqrt(37)#. See explanation.

The Law of Cosines lets you calculate the length of a side having two other sides and the value of cosine of the angle between them:

#d^2=e^2+f^2-2efcosD#

If we substitute the given values we get:

#d^2=8^2+3^2-2*8*3*3/4#

#d^2=64+9-36#

#d^2=73-36=37#

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