Question

15
image.png
15/8
15/17
17/15
8/17
8/15
17/8
tanθ =
sinθ =
cosθ =

Explanation:

Step1: Find the opposite side, adjacent side and hypotenuse

Assume the right - angled triangle has adjacent side \(a = 15\). Let's assume the opposite side \(b\) and hypotenuse \(c\).
We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)
If we assume the Pythagorean triple (8, 15, 17) (since \(8^{2}+15^{2}=64 + 225=289=17^{2}\))
For \(\tan\theta\):
\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)
If the opposite side \(b = 8\) and adjacent side \(a=15\)
\(\tan\theta=\frac{8}{15}\)

Step2: For \(\sin\theta\)

\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)
Since opposite side \(b = 8\) and hypotenuse \(c = 17\)
\(\sin\theta=\frac{8}{17}\)

Step3: For \(\cos\theta\)

\(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)
Since adjacent side \(a = 15\) and hypotenuse \(c = 17\)
\(\cos\theta=\frac{15}{17}\)

Answer:

\(\tan\theta=\frac{8}{15}\), \(\sin\theta=\frac{8}{17}\), \(\cos\theta=\frac{15}{17}\)