Question

Is it True/False? Justify your answer. If angle P and angle Q are acute angles such that sinP=sinQ, then angle P ≠ angle Q.

Answer 1

Given :   angle P and angle Q are acute angles such that sin P=sinQ

To Find : angle P ≠ angle Q​ True or False

Solution:

Lets draw two right angle triangle

MNP  right angle at N   & RSQ right angle at S

(∵ P & Q are acute angles)

Sin∠P  = MN/MP

Sin∠Q = RS/RQ

Sin∠P = Sin∠Q  

=> MN/MP = RS/RQ

& ∠N = ∠S  = 90°

in Δ MNP  & ΔRSQ

Corresponding sides ratio & angle between them is equal

Hence Δ MNP  ≈ ΔRSQ

=> ∠P  =∠ Q    ( Corresponding angles of similar triangle are equal )

Hence angle P ≠ angle Q​   is not True

angle P ≠ angle Q​   FALSE

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