What is measurrment: KIH, JIH, KJI, and HKI?
1 answer:
<h3>Answer:</h3>
- KIH = 52.88°
- JIH = 105.50°
- KJI = 97.61°
- HKI = 43.12°
<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.
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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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