Question

See below to answer this question

Answer 1

Answer: OPTION A.

Step-by-step explanation:

Observe the figure attached.

The first step is the find "a". In order to find this side, we need to use this Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case:

$\alpha=45\°\\\\opposite=12\\\\hypotenuse=a$

Then, substituting values and solving for "a", we get:

$sin(45 \°)=\frac{12}{a}\\\\a=\frac{12}{sin(45 \°)}\\\\a=12\sqrt{2}$

Now we must apply this Trigonometric Identity:

$tan\theta=\frac{opposite}{adjacent}$

In this case:

$\theta=60\°\\\\opposite=12\sqrt{2}\\\\adjacent=x$

Then, substituting values and solving for "x", we get:

$tan(60\°)=\frac{12\sqrt{2}}{x}\\\\x=\frac{12\sqrt{2}}{tan(60 \°)}\\\\x=4\sqrt{6}$

Answer 2

Answer:

c. 6√2

Step-by-step explanation:

The step by step explanation is shown in the picture above