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Anastasy [175]
2 years ago
8

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

Mathematics
1 answer:
Makovka662 [10]2 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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Answer:

1 solution.

General Formulas and Concepts:

<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define equation</u>

9(z + 8) = -9z - 72

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute 9:                              9x + 72 = -9z - 72
  2. Add 9z to both sides:               18z + 72 = -72
  3. Subtract 72 on both sides:       18z = -144
  4. Divide 18 on both sides:           z = -8

Here we see that we will get only 1 solution for <em>z</em>.

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<h2><u>CIRCUMFERENCE</u></h2>

<h3>Possible Question:</h3>

» The diameter of a circle is 11 in. What is the circle's circumference?

<h3>Answer:</h3>
  • \blue{\bold{34.54 \: \:in}}

— — — — — — — — — —

<h3>Step-by-step explanation:</h3>

To find the circumference, use pi (π), a mathematical constant. Its value is approximately equal to 3.14.

— Multiply the diameter with π in order to get the circumference of a Circle.

  • \sf \: given  :  \underline{ \tt \: d = 11 \:  in \: } \\  \\ \tt \: \: C = π × d \tt \\ \tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14×11 \: in  \\ \tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline{ \boxed{ \purple{ \bold{ 34.54\:in}}}}

Therefore, the circumference of the circle is 34.54 inches.

_______________∞_______________

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