Question

Determine the value of x.

Answer 1

Answer:

B

Step-by-step explanation:

According to the leg opposite to 30 degree theorem, the leg opposite to the 30 degree angle is half the length of the hypotenuse. The measurements would be 4, x, 8

We can now use pythagorean theorem.

$8^2-4^2=x^2$

$x^2=64-16$

$x^2=48$

$x=\sqrt{48}$ which is $\sqrt{16*3}$ which is just $4\sqrt{3}$

The answer is B

Answer 2

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = $\frac{\sqrt{3} }{2}$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{8}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 8$\sqrt{3}$ ( divide both sides by 2 )

x = 4$\sqrt{3}$ → B