Question

Please help me i’m so lost Determine the lengths of AB and AC in the right triangle. You may give your answers in radical

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin30° = $\frac{1}{2}$ , cos30° = $\frac{\sqrt{3} }{2}$ , then

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{BC}{AB}$ = $\frac{6}{AB}$ = $\frac{1}{2}$ ( cross- multiply )

AB = 12

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{AC}{AB}$ = $\frac{AC}{12}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2 AC = 12$\sqrt{3}$ ( divide both sides by 2 )

AC = 6$\sqrt{3}$