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in Trigonometry by (48.7k points)
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If cos θ = 15/17, then find sin θ.

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cos θ = 15/17 .. .(i) [Given] 

In right angled ∆ABC, ∠C = θ.

Let the common multiple be k. 

∴ BC = 15k and AC = 17k

Now, AC2 = AB2 + BC2 … [Pythagoras theorem] 

∴ (17k)2 = AB2 + (15K)2 

∴ 289k2 = AB2 + 2252

∴ AB2 = 289k2 – 225k2 

= 64k2 

∴ AB = √(64k2) .. .[Taking square root of both sides] 

= 8k

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