Question

If angleA and angle P are acute angles such that Sin A = Sin p then prove that angleA = angle P.​

Answer 1

Step-by-step explanation:

Given sinA=sinP

∴ BC/AC = RQ/PR

Let BC/RQ = AC/PR =k

BC=kRQ and AC=kPR

Now, AB/PQ= root K²PR²-K²RQ²/ rootPR²-RQ²

AB/PQ= K root PR²-RQ²/ root PR²-RQ²

AB/PQ=K

Therefore AB/PQ=BC/RQ=AC/PR

∴△ABC∼△PQR [By SSS similarity]

∴∠A=∠P

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