Problem

Based on the figure, select all true equations.
\[
\begin{array}{l}
\cos \left(42^{\circ}\right)=\frac{b}{c} \\
\cos \left(48^{\circ}\right)=\frac{b}{c} \\
\sin \left(42^{\circ}\right)=\frac{b}{c} \\
\sin \left(48^{\circ}\right)=\frac{b}{c} \\
\tan \left(42^{\circ}\right)=\frac{b}{a} \\
\tan \left(48^{\circ}\right)=\frac{b}{b}
\end{array}
\]

Answer

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Answer

Using the trigonometric functions, we find the true equations to be: \[\boxed{\cos \left(42^\circ\right)=\frac{b}{c}}\], \[\boxed{\sin \left(48^\circ\right)=\frac{b}{c}}\], and \[\boxed{\tan \left(42^\circ\right)=\frac{b}{a}}\].

Steps

Step 1 :Given a right triangle with angle measures 42°, 48°, and 90°, we can use trigonometric functions to find the true equations.

Step 2 :Using the trigonometric functions, we find the true equations to be: \[\boxed{\cos \left(42^\circ\right)=\frac{b}{c}}\], \[\boxed{\sin \left(48^\circ\right)=\frac{b}{c}}\], and \[\boxed{\tan \left(42^\circ\right)=\frac{b}{a}}\].

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