Chapter 8.6, Problem 44PPS

To determine

To calculate:

The measure of the player’s angle.

Answer to Problem 44PPS

The measure of the player’s angle is the ${28.2}^{\circ }$ .

Explanation of Solution

Given information:

  

Concept used:

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $a,b=$ sides

  $\cos C=$ angle

Calculation:

  

Since, Alyssa is a closer to the goal, so she has a greater chance to make a goal.

Let $x$ be the measure of Alyssa’s angle with the two ends of the post. So, use the law of cosines to get the Alyssa’s shooting angle, as having three sides of the triangle.

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $\begin{array}{l}a=20\\ b=25\\ c=12\\ \cos C=X\end{array}$

First substitute,

  ${\left(12\right)}^2={\left(20\right)}^2+{\left(25\right)}^2-2\left(20\right)\left(25\right)\cos \left(x\right)$

Now simplify,

  $144=400+625-1000\cos \left(x\right)$

Now solve for the $\cos \left(x\right)$

  $0.881=\cos \left(x\right)$

Now, use the inverse cosine ratio

  $x\approx 28.2$

Therefore, the angle is about the ${28.2}^{\circ }$ .