Chapter 8.6, Problem 7CYU

To determine

To calculate:

The length of the bottom edge, or foot of the sail

Answer to Problem 7CYU

The length of the bottom edge or foot of the sail is $47.1$ feet long.

Explanation of Solution

Given information:

  

Concept used:

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C$

Calculation:

  

With given two sides and included angles, solve this problem using the Law of Cosine.

The foot of the sail represented as $x$ .

Law of Cosines:

  $c^2=a^2+b^2-2ab\cos C\mathrm{...}\left(1\right)$

Where,

  $\begin{array}{l}a=55\\ b=62\\ C=47\\ c=x\end{array}$

Put the values in equation (1)

  $\begin{array}{l}{x}^2=a^2+b^2-2ab\cos x\\ x^2={\left(55\right)}^2+{\left(62\right)}^2-2\left(55\right)\left(62\right)\cos \left(47\right)\end{array}$

Simplify the equation:

  $x^2=2217.77$

Take the sq. root of the both sides

  $x=\sqrt{2217.77}$

Simplify the value:

  $x=47.1$

The length of the bottom edge or foot of the sail is $47.1$ feet long.