Chapter 12.5, Problem 8CYU

To determine

To find: The distance between two receivers.

Answer to Problem 8CYU

Distance between two receivers is $12.9$ yards

Explanation of Solution

Given information:

Receiver A turns ${40}^0$ to see Receiver B

Distance between quarterback and Receiver A is $20$ yards

Using law of Cosines we get

  $c^2=a^2+b^2-2ab\cos C$

On substituting values

We get

  $\begin{array}{l}{c}^2=a^2+b^2-2ab\cos C\\ \Rightarrow c^2={16}^2+{20}^2-2\left(16\right)\left(20\right)\cos {40}^0\\ \Rightarrow c^2=256+400-640\left(0.766\right)\\ \Rightarrow c^2=656-490.24\\ \Rightarrow c^2=165.76\\ \Rightarrow c=\sqrt{165.76}\\ \Rightarrow c=12.9\end{array}$

Therefore,

Distance between two receivers is $12.9$ yards