Question

If `sin A = 9/41` compute cos 𝐴 𝑎𝑛𝑑 tan 𝐴

Answer 1

`sin A = 9/41`

`sin A = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 9/41`

Consider the right-angled triangle ABC,

Let x be the adjacent side

By applying Pythagorean

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

41² = 12² + 9²

𝑥² = 412 − 92

𝑥 = 40

`cos A = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 40/41`

`tan A = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝑠𝑖𝑑𝑒" = 9/40`