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In ΔIJK, i = 2.1 inches, mm∠J=103° and mm∠K=13°. Find the length of k, to the nearest 10th of an inch.

User Teilmann
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1 Answer

4 votes

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.

User AJPerez
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