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