Problem

Here is triangle \( \mathbf{A B C} \).
Find the value of each trigonometric ratio:
\[
\tan (C)=
\]
\[
\sin (A)=
\]

Answer

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Answer

Calculate \( \tan(C) = \frac{a}{b} \) and \( \sin(A) = \frac{a}{c} \)

Steps

Step 1 :Write the trigonometric ratios in terms of triangle sides: \( \tan(C) = \frac{\mathrm{opposite}}{\mathrm{adjacent}} \), \( \sin(A) = \frac{\mathrm{opposite}}{\mathrm{hypotenuse}} \)

Step 2 :Label the triangle sides as \( a \), \( b \), and \( c \), where \( a \) is opposite to angle \( A \), \( b \) is opposite to angle \( B \), and \( c \) is opposite to angle \( C \)

Step 3 :Calculate \( \tan(C) = \frac{a}{b} \) and \( \sin(A) = \frac{a}{c} \)

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