#### Question

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

#### Solution

`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

𝐴𝐶^{2} = 𝐴𝐵^{2} + 𝐵𝐶^{2}

41^{2} = 12^{2} + 9^{2}

𝑥^{2} = 412 − 92

𝑥 = 40

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

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

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#### APPEARS IN

Solution If Sin a = 9/41 Compute Cos 𝐴 𝑎𝑛𝑑 Tan 𝐴 Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.