length of AB,BC of scalene triangle ABC are 12,8 rerspectively.the size of angle is 59degree.find the length of side AC

hard to solve without knowing which angle is 59°.

If A or C, 8/sin59° = 12/sin(C or A), so then you can figure B and use law of sines again to get AC.

If B, AC^2 = 8^2 + 12^2 - 2*8*12 cos 59°

7.64

To find the length of side AC, we can use the Law of Cosines for triangles. This law states that for any triangle with sides a, b, and c, and angle C between sides a and b, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, side AB is 12 units long, side BC is 8 units long, and angle C (opposite side AC) measures 59 degrees.

Plugging these values into the Law of Cosines equation, we have:

AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(C)

AC^2 = 12^2 + 8^2 - 2 * 12 * 8 * cos(59°)

Now let's calculate the value of AC:

AC^2 = 144 + 64 - 2 * 12 * 8 * cos(59°)

AC^2 = 208 - 192 * cos(59°)

Using a calculator, we find that cos(59°) is approximately 0.538. Substituting this value, we get:

AC^2 = 208 - 192 * 0.538

AC^2 = 208 - 103.296

AC^2 ≈ 104.704

Taking the square root of both sides, we find:

AC ≈ √104.704

AC ≈ 10.233

Therefore, the length of side AC is approximately 10.233 units.