Question 9 of 18intermediate🔧 ApplyNumerical2 marks

In ΔPQR\Delta PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Correct Answer

sin P = 12/13, cos P = 5/13, tan P = 12/5

Exercise: EXERCISE 8.1 | Q: 10 | (Page Page 9)
For More Understanding

Explanation

This question tests the application of Pythagoras theorem and trigonometric ratios in a right triangle. The student needs to first find the unknown sides using the given conditions, then apply the definitions of trigonometric ratios. The key insight is to express PR in terms of QR (or vice versa) using the given equation PR + QR = 25, then substitute into the Pythagoras theorem to solve for the sides.

Solution Steps

  1. Step 1: Let PR = x and QR = y. Given: x + y = 25 cm and PQ = 5 cm.

  2. Step 2: Apply Pythagoras theorem in ΔPQR: PR² = PQ² + QR², i.e., x² = 5² + y² = 25 + y².

  3. Step 3: Since x = 25 – y, substitute in the equation: (25 – y)² = 25 + y².

  4. Step 4: Expand: 625 – 50y + y² = 25 + y², which gives 625 – 50y = 25, so 50y = 600, therefore y = QR = 12 cm.

  5. Step 5: Then PR = 25 – 12 = 13 cm.

  6. Step 6: Now calculate: sin P = QR/PR = 12/13, cos P = PQ/PR = 5/13, tan P = QR/PQ = 12/5.

PreviousNext