The length of side k, to the nearest tenth of an inch, is approximately 0.5 inches.
How to find the length of side k in triangle IJK
To find the length of side k in triangle IJK, use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we have:
i = 2.1 inches (opposite angle I)
mm∠J = 103° (opposite side J)
mm∠K = 13° (opposite side K)
We can set up the following proportion using the Law of Sines:
i / sin(mm∠I) = k / sin(mm∠K)
Plugging in the given values:
2.1 / sin(103°) = k / sin(13°)
We can solve for k by rearranging the equation:
k = (2.1 * sin(13°)) / sin(103°)
Using a calculator, we find that:
sin(13°) ≈ 0.224951
sin(103°) ≈ 0.97437
k ≈ (2.1 * 0.224951) / 0.97437
k ≈ 0.4841
Therefore, the length of side k, to the nearest tenth of an inch, is approximately 0.5 inches.