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Anastasy [175]
3 years ago
8

What is measurrment: KIH, JIH, KJI, and HKI?

Mathematics
1 answer:
Makovka662 [10]3 years ago
6 0
<h3>Answer:</h3>
  • KIH = 52.88°
  • JIH = 105.50°
  • KJI = 97.61°
  • HKI = 43.12°
<h3>Step-by-step explanation:</h3>

<em>The figure as drawn is impossible</em>. Taking the side lengths to be correct, triangle GIJ can be solved using the Law of Cosines. That solution can be used to solve triangle GJK using the angle at G and the Law of Sines.

The angle GJK, marked as 28°, is actually about 29.7767°.

The size of the angle at H (84°) ensures that the quadrilateral is <em>not cyclic</em>, so the solution of triangle HIK involves three simultaneous quadratic equations in the side lengths HI, GH, and HK (using the Law of Cosines).

I used a machine solver for that, with the results shown above.

_____

The figure shows the same result using a free geometry drawing program, GeoGebra. The tricky part is making sure the angle at H is 84°. That is done by making IK the chord of a circle through points H, I, K, such that the chord subtends an arc of 168°. The angle values shown on the figure are those measured by the drawing program.

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