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

Apr 29, 2017

Using the Law of Cosines we get: $d = \sqrt{37}$. See explanation.

#### 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:

## ${d}^{2} = {e}^{2} + {f}^{2} - 2 e f \cos D$

If we substitute the given values we get:

${d}^{2} = {8}^{2} + {3}^{2} - 2 \cdot 8 \cdot 3 \cdot \frac{3}{4}$

${d}^{2} = 64 + 9 - 36$

${d}^{2} = 73 - 36 = 37$