Question

find c.
triangle with 30°, 60°, right angle, side 19√6 ft, side c
write your answer in simplest radical form.
blank feet

Explanation:

Step1: Identify cosine of 30°

$\cos(30^\circ) = \frac{19\sqrt{6}}{c}$

Step2: Substitute $\cos(30^\circ)$ value

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$, so $\frac{\sqrt{3}}{2} = \frac{19\sqrt{6}}{c}$

Step3: Solve for c via cross-multiplication

$c = \frac{19\sqrt{6} \times 2}{\sqrt{3}}$

Step4: Simplify the radical

$\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2}$, so $c = 19 \times 2 \times \sqrt{2}$

Answer:

$38\sqrt{2}$ feet