(4/3)d^2+5=2

a). d= -2/3 or d= 2/3
b). d= -3/2 or d= 3/2
c). d= -36 or d=36
d). no real solution

D. no real solution.

(4/3)d² + 5 = 2
(4/3)d² = 2 - 5
(4/3)d² = -3
d² = -3 / (4/3)
d² = -3 * 3/4
d² = -9 / 4
d = √-9 / √4
d = -3/2

Even though I got the value of d, when I substituted the value to the equation, the equation is not equal to 2.

I got 8 = 2. not equal. no real solution.

  44.1 cm

Step-by-step explanation:

In order to find the length of side "a", you need to know the measure of angle A. That is found by making use of the fact that the sum of angles in a triangle is 180°.

  102° + 28° + A = 180°

  A = 180° -130° = 50°

Now, you can fill in the given information in the given equation and solve for "a":

  sin(A)/a = sin(B)/b

  sin(50°)/a = sin(28°)/(27 cm)

Multiplying by a(27 cm) gives ...

  sin(50°)(27 cm) = a·sin(28°)

Dividing by the coefficient of "a", we get ...

  a = (27 cm)sin(50°)/sin(28°) ≈ 44.0563 cm

Rounded to the nearest tenth, this is ...

  a ≈ 44.1 cm

Since we're looking for a side length (not an angle), I prefer to write the Law of Sines formula "upside down" from that shown:

  a/sin(A) = b/sin(B) = c/sin(C)

Then it is one step to get to ...

  a = b·sin(A)/sin(B) . . . . . . multiply by sin(A)