Question

1 multiple choice 1 point
what are the values of v and u?
$v=4\sqrt{3}\\ u=4$
$v=8\sqrt{3}\\ u=16$
$v=4\\ u=4\sqrt{3}$
$v=8\\ u=8\sqrt{2}$

Explanation:

Step1: Identify triangle sides/angles

We have a right triangle with:

• Opposite side to $60^\circ$: $v$
• Adjacent side to $60^\circ$: $8$
• Hypotenuse: $u$

Step2: Solve for $v$ using tangent

$\tan(60^\circ) = \frac{v}{8}$
Since $\tan(60^\circ)=\sqrt{3}$,
$v = 8\times\sqrt{3} = 8\sqrt{3}$

Step3: Solve for $u$ using cosine

$\cos(60^\circ) = \frac{8}{u}$
Since $\cos(60^\circ)=\frac{1}{2}$,
$u = \frac{8}{\frac{1}{2}} = 16$

Answer:

$v=8\sqrt{3}\ \ u=16$ (second option)