2007-03-23 23:21:10 · 8 answers · asked by khalid 1 in Science & Mathematics ➔ Mathematics
R=a/2sina=a/2sin60=a/(3)^1/2
a=R*(3^1/2)
=10*3^1/2
area=(3^1/2)/4 *a^2
put the value of a from above
2007-03-23 23:50:23 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The equilateral triangle touches the circle at the length from its center to one end of the circle. Since all points on a circle are equidistant from its center, this length is also 10cm. The length from one point on the triangle to another one is perpendicular to the radius of the circle due to a certain theorem, and this length is also 10cm. Since this is an equilateral triangle, the length from the center to one vertice on the triangle is 10 as well and the angle is bisected because such a line is a part of the median. This makes a 30-60-90 triangle, with a hypotenuse length of 10. The length from the center of the triangle to the midpoint of a side is then 5 because the ratio of the sides is a - a root 3 - 2a. By doing so, the length of the height of the equilateral triangle is 15 (or 10+5). The third side of the 30-60-90 triangle is 5 times the square root of three, but it only represents half of the overall base of the equilateral triangle, so the base is 10 times the square root of three. After that, it is simple math: 1/2 times 10 root three times 15, or A=75root3.
2007-03-25 23:30:17 · answer #2 · answered by renomitsu 3 · 0⤊ 0⤋
The side of the triangle can be found using
the Law of Cosines : c² = a² + b² - 2ab cos C
c² = (10) ² + (10) ² - 2 (10) (10) cos120
c = √300
The area of the equilateral triangle is
A = s² √3 / 4 = 300 √3 / 4 ≈ 130 sq. cm
2007-03-24 00:45:13 · answer #3 · answered by Zax 3 · 0⤊ 0⤋
Find the base of the triangle by using the Law of Cosines
c^2 = a^2 + b^2 - 2ab Cos 120
c^2 = 100 + 100 - 2(10)(10) (-1/2)
c^2 = 300
The height is given by 10 + 10 Sin 30 = 15
The area is given by (1/2) * (15) * sqrt(300)
2007-03-23 23:58:47 · answer #4 · answered by z_o_r_r_o 6 · 0⤊ 0⤋
If you join the centre of the circle to the three vertices of the triangle, we will get three obtuse triangles with included angle 120 degrees and two sides as radii. Then area of each traingle is R^2.Sin(Z)/2
10x10xSin (120)/2= 100X.866/2= 43.3
Total area=3x43.3= 129.9 sqcm
As a formula (3X Sqrt(3)XR^2)/4
2007-03-26 08:34:34 · answer #5 · answered by RAJASEKHAR P 4 · 0⤊ 0⤋
Book
2016-03-29 01:58:14 · answer #6 · answered by Anonymous · 0⤊ 0⤋
its difficult
2007-03-23 23:33:11 · answer #7 · answered by Archangel 3 · 0⤊ 0⤋
129.9038106 cm sq.
Please give me best answer thanks!
2007-03-24 02:03:10 · answer #8 · answered by Anonymous · 0⤊ 0⤋