Question

11 which equation shows a correct trigonometric ratio for angle a in the right triangle below? 1) sin a = \frac{15}{17} 2) tan a = \frac{8}{17} 3) cos a = \frac{15}{17} 4) tan a = \frac{5}{8}

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) for an angle \(\theta\).
For angle \(A\):

• Opposite side to \(A\) is \(BC = 8\) cm.
• Adjacent side to \(A\) is \(AC=15\) cm.
• Hypotenuse is \(AB = 17\) cm.

Step2: Calculate each ratio

• \(\sin A=\frac{BC}{AB}=\frac{8}{17}\)
• \(\tan A=\frac{BC}{AC}=\frac{8}{15}\)
• \(\cos A=\frac{AC}{AB}=\frac{15}{17}\)

Answer:

1. \(\cos A=\frac{15}{17}\)