객관식
Which of the following must be true for two triangles to be congruent by the (Side-Side-Side) criterion?
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7. Non-Right Triangles
Law of Sines
Multiple Choice
Given a triangle with sides , , opposite angles , , respectively, which equation can be used to find using the Law of Sines?
A
B
C
D
검증된 단계별 안내1
Recall the Law of Sines, which states that in any triangle with sides \(a\), \(b\), and \(c\) opposite angles \(A\), \(B\), and \(C\) respectively, the ratio of a side length to the sine of its opposite angle is constant. This can be written as:
\[\frac{a}{\sin\left(A\right)} = \frac{b}{\sin\left(B\right)} = \frac{c}{\sin\left(C\right)}\]
To find an equation to solve for side \(b\), isolate the ratio involving \(b\) and its opposite angle \(B\). This gives:
\[\frac{b}{\sin\left(B\right)} = \frac{a}{\sin\left(A\right)} = \frac{c}{\sin\left(C\right)}\]
Choose one of the other sides and angles to relate to \(b\). Typically, you use side \(a\) and angle \(A\) for convenience, so the equation becomes:
\[\frac{b}{\sin\left(B\right)} = \frac{a}{\sin\left(A\right)}\]
This equation allows you to solve for \(b\) if you know the values of \(a\), \(A\), and \(B\). You can rearrange it to:
\[b = a \times \frac{\sin\left(B\right)}{\sin\left(A\right)}\]
Thus, the correct Law of Sines equation to find \(b\) is:
\[\frac{b}{\sin\left(B\right)} = \frac{a}{\sin\left(A\right)}\]
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