Side A has a length of 12 m, and angle Y is 12°. What is the length of side B (in m)?

1. Break Down the Problem

To find the length of side B in a triangle where we know the length of side A and angle Y, we can use the sine function. Given:

• Length of side A = 12 m
• Angle Y = 12°

Side B can be calculated using the sine law, which relates the lengths of sides of a triangle to the sines of the angles opposite those sides.

2. Relevant Concepts

Using the sine rule, we have: $\frac{A}{\sin(Y)} = \frac{B}{\sin(X)}$ where:

• $A$ is the length of side A (12 m)
• $B$ is the length of side B we want to find
• $Y$ is angle Y (12°)
• $X$ is the angle opposite side B, which we need additional information to determine.

If we assume a right triangle for simplicity and knowing one angle, we can directly use calculations without needing $X$.

3. Analysis and Detail

In a right triangle where $Y$ is small, we would typically consider $A$ opposite to angle $Y$:

Using the sine of angle $Y$: $\sin(12^\circ) \approx 0.2079$ From the sine definition: $A = B \cdot \sin(Y) \implies B = \frac{A}{\sin(Y)} = \frac{12}{\sin(12^\circ)}$

Calculating $B$: $B = \frac{12}{0.2079} \approx 57.742$

4. Verify and Summarize

Calculation of $B$: $B \approx 57.742 \text{ m}$ This result was obtained through the sine rule, confirming a relationship in the triangle.

Final Answer

The length of side B is approximately 57.74 m.