Final answer:
To find the length of side j in triangle ΔJKL, we use the Law of Sines. By substituting the given values into the equation and calculating the values of sine, we find that side j is approximately 89.90 cm long.
Step-by-step explanation:
To find the length of side j in triangle ΔJKL, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we have the length of sides k and l, as well as the measure of angle J. So we can set up the following equation:
sin J / j = sin K / k
Now, we can substitute the given values into the equation:
sin 82° / j = sin K / 87
Since the sum of the angles in any triangle is 180°, we can find angle K by subtracting the measures of angles J and L from 180°:
K = 180° - J - L = 180° - 82° - (180° - J) = J - 98°
Now, substitute the value of K into the equation:
sin 82° / j = sin (82° - 98°) / 87
Now, solve for j:
j = (sin 82° × 87) / sin (82° - 98°)
Calculate the value of sin 82°, sin (82° - 98°), and substitute into the equation:
j ≈ (0.9917 × 87) / (0.9407) ≈ 89.90 cm
Therefore, the length of side j is approximately 89.90 cm.