Question

If \(\tan\theta=\dfrac{15}{8}\), then the value of \(\sin\theta\) will be

• A. \(\dfrac{8}{17}\)
• B. \(\dfrac{8}{15}\)
• C. \(\dfrac{15}{17}\)
• D. \(\dfrac{17}{8}\)

Hint:

From \(\tan\theta=\frac{p}{b}\), set a triangle with legs \(p,b\) to get \(\sin\theta=\frac{p}{\sqrt{p^{2}+b^{2}}}\).

Answer 1

The Correct Option is C

Step 1: Form a right triangle.
Let opposite \(=15\), adjacent \(=8\). Then hypotenuse \(=\sqrt{15^{2}+8^{2}}=\sqrt{289}=17\).
Step 2: Compute sine.
\(\sin\theta=\dfrac{\text{opposite}}{\text{hypotenuse}}=\dfrac{15}{17}\).