I know the length of each side of an isosceles triangle. What is the formula to find the angles?

Question

The sides are each 49.25 inches; the base is 93.5 inches

Answer 1

In all isosceles triangles if you drop a perp. line from the apex you will automatically bisect the base.
This done you will have 2 similar rt. angled triangles with base of 46.75 and hypotenuse of 49.25
The angle opp. the perp. is found by looking up the angle whose cosine is 46.75/49.25 = 0.9492 = 18.3*
Hence, other base angle is 18.3* making base angles sum of 36.6*
Sum of the angles of a triangle is 180*
Hence, Apex angle is 180 - 36.6 = 143.4*

Answer 2

Formula:
An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg).

Answer 3

let the angle in front of 93.5 is A & other two angle be B
now A+2B = 180
& from the ratio A:B = 2:1 (same as ratio of sides)
solve these two equation to get your answer.

Answer 4

You should use the law of cosines to solve. Let's define the sides and the angles as follows:

Let point A and point B be the base points of the triangle and point C as the vertex. Thus,

a = angle at A
b = angle at B
c =angle at C
AB = 93.5
BC = 49.25
AC = 49.25

The law of cosines states that for this given triangle:

AC^2 = BC^2 + AB^2 - 2*AB*BC*cos(c)
AB^2 = BC^2 + AC^2 - 2*BC*AC*cos(b)
BC^2 = AB^2 + AC^2 - 2*AB*AC*cos(a)

Use these equations to solve for each angle. Solving, you get:

a = 18.33 degrees
b = 18.33 degrees
c = 143.33 degrees

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Hope this helps

Answer 5

because it is isosceles

let base be AB and vertex be C AC=BC

cos A = AB/2AC = 93.5/99.5(the reason perpendicualr from C bisects AB)

this can be used to solve A and this is same as B
from this C can be founds

Answer 6

vertex angle .. by law of cosines....
a^2+b^2 = c^2 - 2ab[cos(theta)]
49.25^2 + 49.25^2 = 93.5^2 - (2)(49.25)(49.25) cos(T)
2425.5625 + 2425.5625 = 8742.25 - 4851.125 cos(T)
4851.125 - 8742.25 = -4851.125 cos(T)
-3891.125 = -4851.125 cos(T)
-3891.125 / - 4851.125 = cos(T)
.80210 = cos(T)
cos^-1 (.80210) = 36.6688 degrees

180 - 36.6688 = 143.3312 (sum of base angles)
each base angle = sum / 2 = 71.6656