Chapter 8, Problem 26CT

To determine

To Find : The value of $\angle V$ .

Answer to Problem 26CT

The value of $\angle V$ is 90°.

Explanation of Solution

Given information:

  

  $\Delta RTS$ is a right angle.

RT, RS, VT and VS have the lengths.

Let's calculate the length of ST using Pythagoras Theorem.

In right angled triangle, ΔRTS

  $\begin{array}{l}RS²=RT²+ST²\hfill \\ 17²=8²+ST²\hfill \\ 289=64+ST²\hfill \end{array}$

Simplify further to get,

  $\begin{array}{l}ST²=289–64\hfill \\ ST²=225\hfill \\ ST=15\hfill \end{array}$

In triangle, ΔTVS

  $ST²=225$

Also, the sum of square of other two sides is,

  $\begin{array}{l}VS²+TV²=9²+12²\hfill \\ =81+144\hfill \\ =225\hfill \end{array}$

So it implies that,

  $VS²+TV²=ST²$

Therefore, ΔTVS is right angle triangle and value of $\angle V$ is 90°.