In right angle triangle pqr angle q is equals to 90 degree ,angle r is equals to theta and sin theta is equals to 5/13 then find t

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1. Take the given trigonometric ratio as 13k equation (i).

   sin θ = 5/13 .. .(i) [Given]

   By using the definition write the trigonometric ratio of sin θ and take it as equation

   (ii). In right angled ∆PQR, ∠R = θ Let the common multiple be k.

   ∴ PQ = 5k and PR = 13k

   Find QR by using Pythagoras theorem. PR2 = PQ2 + QR2 … [Pythagoras theorem]

   ∴ (13k)2 = (5k)2 + QR2

   ∴ 169k2 = 25k2 + QR2

   ∴ QR2 = 169k2 – 25k2 = 144k2

   ∴ QR = √(144k2) . . . [Taking square root of both sides] = 12k

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