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2 years ago

A circle is inscribed in an equilateral triangle with a side length measuring 10 mm.

Mathematics

1 answer:

Tamiku [17]2 years ago

8 0

For side length s the area of the triangle is
.. A = (√3)/4*s^2
The radius of the circle will be
.. r = s/(2√3)
so the area of the circle is
.. A = π*r^2 = π*s^2/12

The fraction of the triangle that is not in the circle is
.. 1 - (π/12)/((√3)/4)
.. = 1 -π/(3√3)
.. ≈ 39.54%

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Step-by-step explanation:

The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...

s = √(a² +b² -2ab·cos(C))

s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}

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