Question

find each trig ratio.

\\( \sin c = \\)
\\( \cos c = \\)
\\( \tan c = \\)

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)

For \(\angle C\):

• The side opposite to \(\angle C\) is \(AB = 35\)
• The side adjacent to \(\angle C\) is \(BC=12\)
• The hypotenuse is \(AC = 37\)

Step2: Calculate \(\sin C\)

\(\sin C=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{AB}{AC}\)
\(\sin C=\frac{35}{37}\)

Step3: Calculate \(\cos C\)

\(\cos C=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{BC}{AC}\)
\(\cos C=\frac{12}{37}\)

Step4: Calculate \(\tan C\)

\(\tan C=\frac{\text{opposite}}{\text{adjacent}}=\frac{AB}{BC}\)
\(\tan C=\frac{35}{12}\)

Answer:

\(\sin C=\frac{35}{37}\), \(\cos C=\frac{12}{37}\), \(\tan C=\frac{35}{12}\)