Question

which of the following statements is true about \\( \angle p \\), as shown in the right triangle above?
a \\( \cos p = \frac { 5 } { 17 } \\)
b \\( \cos p = \frac { 1 } { 3 } \\)
c \\( \sin p = \frac { 15 } { 17 } \\)
d \\( \tan p = \frac { 1 } { 3 } \\)
e \\( \tan p = 1 \\)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), and \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) for an angle \(\theta\). For \(\angle P\), the adjacent side is \(15\), the opposite side is \(5\), and the hypotenuse is \(17\).

Step2: Calculate \(\cos P\), \(\sin P\), and \(\tan P\)

• \(\cos P=\frac{15}{17}\) (adjacent to \(P\) is \(15\), hypotenuse is \(17\))
• \(\sin P=\frac{5}{17}\) (opposite to \(P\) is \(5\), hypotenuse is \(17\))
• \(\tan P=\frac{5}{15}=\frac{1}{3}\) (opposite to \(P\) is \(5\), adjacent to \(P\) is \(15\))

Answer:

D. \(\tan P=\frac{1}{3}\)