### Question No:1:

In Δ ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine : (i) sin A, cos A (ii) sin C, cos C### Solution:

Let us draw a right angle ΔABC ,right angle at BThe

**Pythagoras theorem**, also known as the

**Pythagorean theorem**, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the

**right-angled triangle**

So, \( A{C^2} = A{B^2} + B{C^2} \)

\( A{C^2} = {(24)^2} + {(7)^2} \)

\( A{C^2} = 576 + 49 = 625 \)

\( \Rightarrow AC = \sqrt {625} = 25cm \)

(i) sin A = \( {{BC} \over {AC}} = {7 \over {25}} \)

Sin∠A = \( \frac{Opposite\; to\; Angle “A”}{ hypotenuse} \)

cos A =\( {{AB} \over {AC}} = {{24} \over {25}} \)

cos∠A = \( \frac{Adjacent\;to\; Angle “A”}{ hypotenuse} \)

(ii) From the Diagram

sin C =\( {{AB} \over {AC}} = {{24} \over {25}}\)

cos C = \( {{BC} \over {AC}} = {7 \over {25}}. \)