Krishna
0

Step 1: According to the given measurements make a right triangle diagram.

          CONSTRUCTION:

                

Step 2: Find the unknown length of the triangle

            NOTE: Use the Pythagoras theorem

                         RQ^2 = QP^2 + PR^2

                         25^2 = 7^2 + PR^2

                         PR^2 = 625 - 49

                         PR = \sqrt{576}

                                  PR = 24 cm


Step 3: Find the trigonometric ratios by substituting the appropriate lengths

               \tan Q = \frac{opposite}{adjacent} = \frac{PR}{QP} = \frac{24}{7}

               \tan R = \frac{opp}{adj} = \frac{QP}{PR} = \frac{7}{24}

                

            Therefore, \tan Q - tan R   (Since Given)

                           =    \frac{24}{7} - \frac{7}{24}

                                          =   \frac{576 - 49}{168}

                                                        =   \frac{527}{168}