Chapter 12.6, Problem 13WE

To determine

To determine the length of chord AC.

Answer to Problem 13WE

Length of chord AC is 7.83

Explanation of Solution

Given information :

  $\angle ABC={26}^{\circ }10\text{'}$

First we shall convert the angle into degrees.

  ${26}^{\circ }10\text{'}={26}^{\circ }+{\left(\frac{10}{60}\right)}^{\circ }={26.16}^{\circ }$

Now we shall make diagram.

  

Use cosine law to determine the length.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Putting values we get,

  $\begin{array}{l}\cos {26.16}^{\circ }=\frac{{10.1}^2+{15.5}^2-{\left(AC\right)}^2}{2\left(10.1\right)\left(15.5\right)}\\ 281=342.26-{\left(AC\right)}^2\\ A{C}^2=61\\ AC=7.83\end{array}$

Hence length of chord AC is 7.83