The sides of a right angle triangle PQR are PQ = 7 cm, QR = 25cm and \angle Q = 90 respectively. Then find, \tan Q - \tan R

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}