How do you find the height of an equilateral triangle inscribed in a circle?

Using the properties of 30˚−60˚−90˚ triangles, it can be determined that h=1 and s2=√3 . Thus, s=2√3 and the height of the triangle can be found through a+h=2+1=3 . Note that the height can also be found through using s and s2 as a base and the hypotenuse of a right triangle where the other leg is 3 .

How do you find the height of a triangle in a circle?

Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!

What is the formula for the height of equilateral triangle?

and the equation for the height of equilateral triangle look as follows: h = a * √3 / 2 , where a is a side of the triangle.

What is the length of an equilateral triangle inscribed in a circle?

Length BD=length DC. Total length BC= BD+DC. BC=2×3√3=6√3cm. Note: If the question was given for isosceles triangle instead of equilateral triangle, the OA≠OB≠OC ≠radius.

What is the relation between circle and equilateral triangle?

Properties of a Circumcircle are as follows:

Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle. The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where 'a' is the length of the side of equilateral triangle.

IMPORTANT Area of Equilateral Triangle Inscribed in a Circle of Radius R

What is the area of an equilateral triangle whose inscribed circle has radius?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa²/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

How do you find the height of an equilateral triangle with side 2a?

What is the height of an equilateral triangle having each side 12cm?

Let ABC be the equilateral triangle with AD as an altitude from A meeting BC at D. Then D will be the midpoint of BC. Applying Pythagoras theorem in right-angled triangle ABD we get:Hence the height of the given triangle is 6√3 cm. समबाहु त्रिभुज की ऊँचाई ज्ञात करें जिसकी प्रत्येक भुजा 12cm है ।

When a triangle is inscribed in a circle?

When a circle inscribes a triangle, the triangle is outside of the circle and the circle touches the sides of the triangle at one point on each side. The sides of the triangle are tangent to the circle. draw in the angle bisectors. The intersection of the angle bisectors is the center of the inscribed circle.

What is the height of an equilateral triangle with sides of 6?

Answer: The height of the given equilateral triangle is 3√3 cm.

What is the height of the equilateral triangle whose side is 10 cm?

you get x^2 + 5^2 = 10^2 which becomes x^2 + 25 = 100 which becomes x^2 = 75 which becomes x = sqrt(75). that's the length of your altitude. you can simplify that to make it 5*sqrt(3).

What is the height of an equilateral triangle whose side is a CM?

Answer. According to the Pythagorean theorem (Hypotenuse)2=(Perpendicular)2+(Base)2. Hence, the length of the altitude of the triangle whose side is equal to 10 cm and the triangle is equilateral triangle will be 5√3cm.

What is the height of an equilateral triangle having side 4a?

2 √3 aВ.

What is the altitude of equilateral triangle of side 8 cm?

Summary: The altitude of an equilateral triangle of side 8 cm is 4√3 cm.

Is an equilateral triangle of side 2a then length of one of its altitude is?

1 Answer. ABC is an equilateral triangle of side 2a, then length of one of its altitude is √3 a.

What is the formula of inscribed circle?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 .

What is the formula for height?

Given triangle area

area = b * h / 2 , where b is a base, h - height. so h = 2 * area / b.