Chapter 6.4, Problem 16WE

To determine

To complete: for angle 1, 2 and 3.

Answer to Problem 16WE

  $m\angle 3>m\angle 2>m\angle 1$

Explanation of Solution

Given:

The diagram is shown below:

  

Side AB is equal to AC .

Calculation:

Consider right triangle ABC .

  $\begin{array}{c}A{B}^2+A{C}^2=B{C}^2\\ A{B}^2+A{B}^2={98}^2\\ 2A{B}^2=9604\\ AB=69.3\end{array}$

Consider the sides BC , BD and AB ,

  $\begin{array}{l}BC=98\\ BD=97\\ AB=69.3\\ \therefore BC>BD>AB\end{array}$

Angle 1, 2 and 3 are opposite to sides AB , BD and BC respectively. Angle opposite to greater side is greater and angle opposite to smaller side is smaller.

Hence,

  $m\angle 3>m\angle 2>m\angle 1$