The measure of an angle of an isosceles triangle is 30°, the shorter side is 20 in. find a distance from point p to the vertex of a triangle, if p is equidistant from all vertices.

the angles in this triangle are 30, 30, and 120. the shorter sides are 20 inches. if P is equidistant from all vertices, it has to be outside of the triangle. We can name the points in the triangle A, B, and C.

You get a quadrilateral if you connect the lines from P to B and P to C. You can get two isosceles triangles from this, APC and APB. In triangle APC, lines AP and CP are equal, and in triangle APB lines AP and BP are equal. The base sides in each of these triangles are 20 inches, and the base angles are 60 degrees, meaning these are equilateral triangles.

HENCE, PA IS EQUAL TO 20 INCHES.

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step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet