Question

I need help with this practice I attempted this and got 13.96? Make sure your answer is rounded to the nearest hundredth

Answer 1

Law of Cosines

Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:

`c^2=a^2+b^2-2ab\cos \theta`

We have a = 14, b = 9, θ = 71°. Substituting:

`\begin{gathered} c^2=14^2+9^2-2\cdot14\cdot9\cos 71^o \\ c^2=196+81-252\cdot0.325568 \\ c^2=194.956825 \\ c=\sqrt[]{194.956825} \\ c=13.96 \end{gathered}`

The length of CD is 13.96