Question

In a ΔABC , ∠B = 90° , AB= 24 cm and BC = 7 cm find (i) sin A (ii) cos A (iii) sin C (iv) cos C

Answer 1

Using Pythagoras theorem, we get:
`AC^2 = AB^2 + BC^2`
`⟹ AC^2 = (24)^2 + (7)^2`
`⟹ AC^2 = 576 + 49 = 625`
⟹ 𝐴𝐶 = 25 𝑐𝑚
Now, for T-Ratios of ∠𝐴, 𝑏𝑎𝑠𝑒 = 𝐴𝐵 𝑎𝑛𝑑 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 𝐵𝐶

(i) sin A = `(BC)/(AC) = 7/25`

(ii) cos A = `(AB)/(AC)=24/25`

Similarly, for T-Ratios of ∠𝐶, 𝑏𝑎𝑠𝑒 = 𝐵𝐶 𝑎𝑛𝑑 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 𝐴𝐵

(iii) sin C = `(AB)/(AC)=24/25`

(iv) cos C= `(BC)/(AC)=7/25`