Question: 6. Find the value of the trigonometric ratios in lowest terms. a) J \[ \sin(J) = \frac{16}{34}…

6. Find the value of the trigonometric ratios in lowest terms.

a) J \[ \sin(J) = \frac{16}{34} \] \[ \sin(L) = \] \[ \cos(J) = \frac{30}{34} \] \[ \cos(L) = \] \[ \tan(J) = \frac{16}{30} \] \[ \tan(L) = \]

[Diagram]

• Triangle with sides labeled:
  • Hypotenuse: 34 ft
  • Opposite side to angle J: 16 ft
  • Adjacent side to angle J: 30 ft

Solution

To find the trigonometric ratios for angle \(L\), we use the triangle \(JKL\) given where: - \(JK = 16 \, \text{ft}\) (opposite to \(J\), adjacent to \(L\)) - \(KL = 30 \, \text{ft}\) (adjacent to \(J\), opposite to \(L\)) - \(JL = 34 \, \text{ft}\) (hypotenuse) Let’s calculate the trigonometric ratios for angle \(L\): 1. \(\sin(L)\): \[ \sin(L) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{30}{34} \] Simplify the fraction: \[ \sin(L) = \frac{15}{17} \] 2. \(\cos(L)\): \[ \cos(L) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{16}{34} \] Simplify the fraction: \[ \cos(L) = \frac{8}{17} \] 3. \(\tan(L)\): \[ \tan(L) = \frac{\text{opposite}}{\text{adjacent}} = \frac{30}{16} \] Simplify the fraction: \[ \tan(L) = \frac{15}{8} \]