In ΔOPQ, right-angled at P, OP = 7 cm and OQ − PQ = 1 cm. Determine the values of sin Q + cos Q.

Explanation

Given In ΔOPQ, right-angled at P, OP = 7 cm and OQ - PQ = 1 cm. Formula used sin Q = P/H and cos Q = B/H Calculation Since it is a right-angled triangle, OQ2 = OP2 + PQ2 ⇒ OQ2 - PQ2 = OP2 ⇒ (OQ - PQ)(OQ + PQ) = 72 ⇒ ( 1)( OQ + PQ ) = 72 ⇒ ( OQ + PQ ) = 49 OQ = (49 + 1)/2 = 25 PQ = (49 - 1)/2 = 24 sin Q = P/H = 7/25 cos Q = B/H = 24/25 sin Q + cos Q = 7/25 + 24/25 = 31/25 The answer is 31/25