If angle B and Q are acute angles such that B=sinQ, prove that angle B= angle Q
Given:
B and Q are acute angles such that B=sinQ
To Prove: ∠B = ∠Q
Answer:
Take two similar triangles ABC and QPR.
In similar triangles the corresponding sides of the triangles are proportional, meaning the ratios of corresponding sides are equal.
The corresponding sides pairs of these triangles are AB, PQ; BC, QR, and AC, PR
Let us take k as the ratio of corresponding sides of these two similar triangles
So $\frac{AC}{PR} = \frac{AB}{PQ}$ = k
The corresponding angles of similar triangles are equal.
i.e., ∠A = ∠P; ∠B = ∠Q; ∠C = ∠R
∠B = ∠Q ( corresponding angles of similar triangles)
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