Question: 6. Find the value of the trigonometric ratios for the indicated lowest terms. a) \(\sin(J) = \)…

6. Find the value of the trigonometric ratios for the indicated lowest terms.

a) \(\sin(J) = \)

\[ \begin{array}{c} \text{Hyp} \\ \text{16 ft} \\ \text{opp} \\ \text{K} \\ \text{30 ft} \\ \text{adj} \\ \text{L} \end{array} \]

\(\cos(J) = \)

Solution

To find the trigonometric ratios for the angle \( J \) in the right triangle, we use the definitions of sine and cosine. 1. Identify the sides: - Opposite to angle \( J \): \( 16 \) ft - Adjacent to angle \( J \): \( 30 \) ft - Hypotenuse: \( 34 \) ft 2. Calculate \(\sin(J)\): \[ \sin(J) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{16}{34} \] 3. Simplify \(\sin(J)\): \[ \sin(J) = \frac{8}{17} \] 4. Calculate \(\cos(J)\): \[ \cos(J) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{30}{34} \] 5. Simplify \(\cos(J)\): \[ \cos(J) = \frac{15}{17} \] So, the trigonometric ratios are: - \(\sin(J) = \frac{8}{17}\) - \(\cos(J) = \frac{15}{17}\)