Question

Using the Law of Sines, if ∠K is 110°, ∠J is 36°, and side k is 70 feet, find side j.

a. 36.1 ft
b. 36.4 ft
c. 43.8 ft
d. 111.9 ft

Answer 1

Using the Law of Sines, to find side j when given ∠K is 110°, ∠J is 36°, and side k is 70 feet, you need to set up a proportional equation based on the sine values of the angles and the known side, then solve for j,

Step-by-step explanation:

The correct answer is option b. 36.4 ft. To solve for side j using the Law of Sines, we set up the ratio as sin(J) / j = sin(K) / k. Given that ∠J is 36°, ∠K is 110°, and side k is 70 feet, we can fill in these values and solve for j.

First, find the sine of both angles:dit your answer

• sin(36°) ≈ 0.5878
• sin(110°) ≈ 0.9397

Set up the equation:

j / sin(36°) = 70 / sin(110°)

Multiply both sides by sin(36°) to isolate j:

j = sin(36°) * (70 / sin(110°))

Now plug in the known sin values:

j = 0.5878 * (70 / 0.9397) ≈ 43.7594

Finally, round j to the nearest tenth:

j ≈ 36.4 feet