Question

2. If angleA and angleP are acute angles such
that sin A = sin P, then prove that
angle A = angleP​

Answer 1

Answer:

i gave the ans for angle b and angle q

∴ AC = k × PR and AB = k × PQ

From right ΔACB, by Pythagoras theorem we have

AB2 = AC2 + BC2

⇒ (k × PR)2 = (k × PQ) 2 + BC2

⇒ k2 × PR2 = k2 × PQ2 + BC2

⇒ BC2 = k2 × PR2 – k2 × PQ2

= k2[PR2 – PQ2]

From right ΔPRQ, by Pythagoras theorem we have

PQ2 = PR2 + QR2

⇒ QR2 = PQ2 – PR2

Hence ΔACB ~ ΔPRQ (SSS similarity criterion)

∴ ∠B = ∠Q

Step-by-step explanation:

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