Question

12 in the diagram below of right triangle abc, ac = 8, and ab = 17. which equation would determine the value of angle a? 1) sin a = \frac{8}{17} 2) tan a = \frac{8}{15} 3) cos a = \frac{15}{17} 4) tan a = \frac{15}{8}

Explanation:

Step1: Find the length of \(BC\)

Using the Pythagorean theorem \(AB^{2}=AC^{2}+BC^{2}\). Substitute \(AB = 17\) and \(AC=8\):

$$\begin{align*} 17^{2}&=8^{2}+BC^{2}\\ 289&=64 + BC^{2}\\ BC^{2}&=289 - 64\\ BC^{2}&=225\\ BC& = 15 \end{align*}$$

Step2: Recall trigonometric ratios

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

Answer:

1. \(\tan A=\frac{15}{8}\)