Given a right triangle with angle $A$ equal to $50°$ and hypotenuse $c$, which equation can be used to solve for $c$ if the side opposite angle $A$ is $a$ and the side adjacent is $b$?

• A. $c=\frac{b}{cos(50°)}$
• B. $c=\frac{a}{sin(50°)}$
• C. $c=\frac{a}{cos(50°)}$
• D. $c=\frac{b}{sin(50°)}$

Answer: (B)

Verified step by step guidance

1. Identify the sides relative to angle A in the right triangle: side a is opposite angle A, side b is adjacent to angle A, and side c is the hypotenuse.
2. Recall the definition of sine in a right triangle: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\). For angle A, this becomes \(\sin(50^\circ) = \frac{a}{c}\).
3. Rearrange the sine equation to solve for the hypotenuse c: multiply both sides by c and then divide both sides by \(\sin(50^\circ)\) to isolate c, giving \(c = \frac{a}{\sin(50^\circ)}\).
4. Verify that using cosine would relate the adjacent side b to the hypotenuse c by \(\cos(50^\circ) = \frac{b}{c}\), which rearranges to \(c = \frac{b}{\cos(50^\circ)}\), but since the problem asks for the equation involving side a, the sine relation is appropriate.
5. Conclude that the correct equation to solve for c using the opposite side a and angle 50° is \(c = \frac{a}{\sin(50^\circ)}\).