Question

find \\(\sin\theta\\), where \\(\theta\\) is the angle shown. give an exact value, not a decimal approximation. the right triangle has one leg 15, another leg 8, and angle \\(\theta\\) at the vertex with the leg of length 8. \\(\sin\theta = \\) blank

Explanation:

Step1: Find the hypotenuse

Using the Pythagorean theorem \( c = \sqrt{a^2 + b^2} \), where \( a = 8 \) and \( b = 15 \).
\( c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \).

Step2: Calculate \( \sin\theta \)

In a right triangle, \( \sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} \). The side opposite \( \theta \) is 15, and the hypotenuse is 17.
\( \sin\theta = \frac{15}{17} \).

Answer:

\( \frac{15}{17} \)