Exercise 8.1 Q10 | In △ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values

NCERT Class 10 Maths Chapter 8, Exercise 8.1, Q10: In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine sin P, cos P, and tan P.

In this video, we solve Question 10 from Exercise 8.1. This is a unique problem because it combines trigonometry with a bit of algebra. Instead of being given all the sides, we are given the sum of two sides, and we must use the Pythagoras Theorem to find them individually.

Step-by-Step Solution Breakdown:
1. Identify Given Information:

Triangle PQR is right-angled at Q.

PQ = 5 cm

PR + QR = 25 cm

2. Set up the Algebra:
Let QR = x.
Then, PR = 25 - x (since their sum is 25).

3. Apply Pythagoras Theorem:
In triangle PQR, PR² = PQ² + QR².

(25 - x)² = 5² + x²

625 - 50x + x² = 25 + x²

625 - 25 = 50x

600 = 50x

x = 12

4. Final Side Lengths:

QR = 12 cm

PR = 25 - 12 = 13 cm

PQ = 5 cm (Given)

5. Calculate the Ratios for Angle P:

sin P = Opposite / Hypotenuse = QR / PR = 12/13

cos P = Adjacent / Hypotenuse = PQ / PR = 5/13

tan P = Opposite / Adjacent = QR / PQ = 12/5

Topics Covered:
Solving NCERT Exercise 8.1 Question 10

Using algebra to find missing sides in trigonometry

Pythagoras Theorem applications

Finding sin, cos, and tan for Class 10 Board Exams

Key Formulas Used:
Pythagoras Theorem: H² = P² + B²

Algebraic Identity: (a - b)² = a² - 2ab + b²

sin P = P / H | cos P = B / H | tan P = P / B

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Видео Exercise 8.1 Q10 | In △ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values канала Gyaani Jagat