Chapter 9.7, Problem 27PSD

To determine

To calculate: Length of CE.

Answer to Problem 27PSD

Length of CE is $12$ units.

Explanation of Solution

Given information:Here, we have that $\angle ACB$ is a right angle, $\overrightarrow{CD}$ and $\overrightarrow{CE}$ trisect $\angle ACB$ . AC = $5$ and BC = $12$

Formula used: Sum of all interior angles of a triangle is $180°$ .

Calculation: Draw a perpendicular from E to CB such that $EF\perp CB$ .

As, $\overrightarrow{CD}$ and $\overrightarrow{CE}$ trisect $\angle ACB$ ,

  $\Rightarrow \angle BCE=\angle ECD=\angle DCA=30°$

Now, in $\Delta EFC$ ,

  $\begin{array}{l}\angle ECF+\angle EFC+\angle CEF=180°\\ \Rightarrow 30°+90°+\angle CEF=180°\\ \Rightarrow 120°+\angle CEF=180°\\ \Rightarrow \angle CEF=180°-120°\\ \Rightarrow \angle CEF=60°\end{array}$

Now, angles in $\Delta EFC$ are $90°,60°,30°$

  $\Rightarrow$ Hypotenuse = 2a and Perpendicular = a

Here, perpendicular (FC) = a = $6$

  $\Rightarrow$ Hypotenuse (CE) = $2a=2(6)=12$ units