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 B
The 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 = \( {{BC} \over {AC}} = {7 \over {25}} \)


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


(ii) From the Diagram

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

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