In right triangle $△abc$, if side $ac$ = $5$ mm, side $ab$ = $3$ mm, and side $bc$ = $4$ mm, what is $\sin a$?

• A. $\frac{4}{3}$
• B. $\frac{3}{5}$
• C. $\frac{5}{4}$
• D. $\frac{4}{5}$

Answer: (B)

Verified step by step guidance

1. Identify the right angle in triangle ABC. Since it is a right triangle, one of the angles is 90 degrees. Typically, the side opposite the right angle is the hypotenuse.
2. Determine which side is the hypotenuse. The hypotenuse is the longest side, so here side AC = 5 mm is the hypotenuse.
3. Recall the definition of sine for an angle in a right triangle: \(\sin(\angle A) = \frac{\text{length of side opposite to } A}{\text{length of hypotenuse}}\).
4. Identify the side opposite to angle A. Since angle A is at vertex A, the side opposite to it is BC, which has length 4 mm.
5. Substitute the values into the sine formula: \(\sin(\angle A) = \frac{4}{5}\). This fraction represents the sine of angle A.