In triangle ABC angle a equals 72° side C equals 61 and angle B equals 16° find side a to the nearest 10th

  58.0 units

Step-by-step explanation:

In order to use the law of sines, we need to know angle C. It will be the angle that brings the total of all angles to 180°.

  C = 180° -A -B = 180° -72° -16°

  C = 92°

The law of sines tells us ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = 61·sin(72°)/sin(92°)

  a ≈ 58.0 . . . . units

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.