Question

5 multiple choice 1 point in △abc, which of the following is equal to \\( \frac { 12 } { 13 } \\)? tan c sin c cos c cos a

Explanation:

Step1: Recall trigonometric ratios

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

Step2: Analyze for angle \(C\)

For \(\angle C\), the opposite side is \(AB = 5\), the adjacent side is \(BC=12\), and the hypotenuse is \(AC = 13\)

• \(\tan C=\frac{AB}{BC}=\frac{5}{12}\)
• \(\sin C=\frac{AB}{AC}=\frac{5}{13}\)
• \(\cos C=\frac{BC}{AC}=\frac{12}{13}\)

Step3: Analyze for angle \(A\)

For \(\angle A\), the opposite side is \(BC = 12\), the adjacent side is \(AB = 5\), and the hypotenuse is \(AC=13\)

• \(\cos A=\frac{AB}{AC}=\frac{5}{13}\)

Answer:

\(\cos C\)