Chapter 9.9, Problem 22PSC

To determine

To find:The value of $\tan \angle KEI$

Answer to Problem 22PSC

The value of $\tan \angle KEI=\frac{3\sqrt{2}}{\sqrt{31}}$

Explanation of Solution

Given information:The following information has been given

  $KI=IT=6$

  $KE=ET=7$

O is the midpoint of diagonals of KITE

Formula used:Pythagoras theorem has been used

Calculation:We apply Pythagoras theorem in the triangles KIO and KEO individually, we get

  $KO=OI=3\sqrt{2}$ , and

  $OE=\sqrt{31}$

Now, we know that

  $\tan \angle KEI=\tan \angle KEO=\frac{KO}{EO}=\frac{3\sqrt{2}}{\sqrt{31}}$

Hence, we get

  $\tan \angle KEI=\frac{3\sqrt{2}}{\sqrt{31}}$