Find the diameter of the largest circular pond that could fit in a triangular garden with vertices at (18,54), (-27,36), & (27,-18), where a unit represents 1m.

The diameter of the largest circular pond that could fit in a triangular garden with vertices at (18,54), (-27,36), & (27,-18) is 34.5m.

Explanation:

Let the vertices of the triangle are A(18,54), B(-27,36), & C(27,-18).

Use distance formula to find the length of sides.

Using the above formula the distance between AB is 48.5, BC is 76.4 and AC is 72.6.

The length of sides are 48.5, 76.4 and 72.6.

Formula to find semi-perimeter is given below,

Where a, b and c are the length of sides.

The formula to find the radius of the circle pond in the triangle is given below,

The radius of the circle is 17.25 m.

Therefore, the diameter of circle is 34.5 m.

21

jk it's 20

step-by-step explanation:

arc length = 6.63311 ft.

step-by-step explanation:

the formula the arc measure is:

arc length s=2πr(c)/360

where:

c   is the central angle of the arc in degrees

r   is the radius of the arc

π   is pi, approximately 3.142

using the above formula we get

s =

thus we find that arc length of an arc for a circle of radius 20 feet and central angle 19 degrees is

6.63311 feet