If $\angle B$ and $\angle Q$ are acute angles such that $\sin B = \sin Q$, then prove that $\angle B = \angle Q$.

Step 1: Define acute angles and sine function

Acute angles are angles whose measures are greater than $0^\circ$ and less than $90^\circ$. The sine function relates an angle of a right-angled triangle to the ratio of the length of the opposite side to the length of the hypotenuse.

Step 2: Consider the given condition

We are given that the sine of angle $B$ is equal to the sine of angle $Q$.

Step 3: Analyze the sine function for acute angles

The sine function is strictly increasing in the interval $[0^\circ, 90^\circ]$. This means that for any two distinct acute angles, their sines will be distinct. Therefore, if the sines of two acute angles are equal, the angles themselves must be equal.

Step 4: Conclude the proof

Since both $\angle B$ and $\angle Q$ are acute angles, and their sines are equal $(\sin B = \sin Q)$, it logically follows that the angles themselves must be equal.

More from this chapter

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