7. Solve for the side length of BA and AC.

Question

Triangle ABC Is a right triangle with A being the 90* angle and C being 30* And BC length being 16
BA = 8, BA = 30
BA = 8, AC = 16
BA = 8, AC = 8√2
BA = 8, AC = 8√3

Answer 1

To solve for the side lengths of BA and AC, we can use trigonometric ratios.

Given that angle C is 30 degrees, we can use the trigonometric ratio for a 30-60-90 triangle:

sin(30 degrees) = opposite/hypotenuse
sin(30 degrees) = AC/16

By solving for AC, we get:
AC = 16*sin(30 degrees)
AC = 16*(1/2)
AC = 8

Therefore, the length of AC is 8.

Since triangle ABC is a right triangle, we can use the Pythagorean theorem to find the length of BA:
BA^2 + AC^2 = BC^2
BA^2 + 8^2 = 16^2
BA^2 + 64 = 256
BA^2 = 192
BA = √192
BA = √(64*3)
BA = 8√3

Therefore, the length of BA is 8√3 and the length of AC is 8.