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What is the area of an equilateral triangle inscribed in a circle with a radius of 5 inches?

Answer 1

Evelyn Arboleda

#(50 + 50 * 1 / 2) sqrt 3 / 4#

#Delta ABC# is equilateral. #O# is the center.

#|OA| = 5 = |OB|#

#A hat O B = 120º = (2 pi) / 3#

Cossin Law: #|AB|^2 = 5^2 + 5^2 - 2 * 5^2 cos 120º = L^2#

#A_Delta = L^2 sqrt 3 / 4#

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Answer 2

Sadie Allen

To find the area of an equilateral triangle inscribed in a circle with a radius of 5 inches, we can use the formula for the area of an equilateral triangle, which is (\frac{{\sqrt{3}}}{4} \times \text{{side length}}^2).

The side length of the equilateral triangle is equal to the diameter of the circle, which is twice the radius. So, the side length is (2 \times 5 = 10) inches.

Substituting this value into the formula, we get:

Area of equilateral triangle = (\frac{{\sqrt{3}}}{4} \times 10^2)

= (\frac{{\sqrt{3}}}{4} \times 100)

= (\frac{{100\sqrt{3}}}{4})

= (25\sqrt{3}) square inches.

Therefore, the area of the equilateral triangle inscribed in a circle with a radius of 5 inches is (25\sqrt{3}) square inches.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.