Question

Find the missing lengths of the sides

Answer 1

Answer: option c

Step-by-step explanation:

You can use these identities:

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

Then, using the angle that measures 30 degrees, you know that:

$\alpha=30\°\\opposite=8\\adjacent=b$

Substituting:

$tan(30\°)=\frac{8}{b}$

Now you must solve for b:

$b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}$

Using the angle that measures 30 degrees, you know that:

$\alpha=30\°\\opposite=8\\hypotenuse=c$

Substituting:

$sin(30\°)=\frac{8}{c}$

Now you must solve for c:

$c=\frac{8}{sin(30\°)}\\\\c=16$

Answer 2

ANSWER

The correct answer is C

EXPLANATION

The side adjacent to the 60° angle is 8 units.

The hypotenuse is c.

Using the cosine ratio, we have

$\cos(60 \degree) = \frac{adjacent}{hypotenuse}$

$\cos(60 \degree) = \frac{8}{c}$

$\frac{1}{2}= \frac{8}{c}$

Cross multiply

$c = 8 \times 2 = 16$

Also

$\cos(30 \degree) = \frac{b}{c}$

$\cos(30 \degree) = \frac{b}{16}$

$\frac{ \sqrt{3} }{2} = \frac{b}{16}$

Multiply both sides by 16

$b = 16 \times \frac{ \sqrt{3} }{2}$

$b = 8 \sqrt{3}$

The correct answer is C