For the right Triangle below, Find the exact values of the side lengths c and a. If necessary, write your response in simplified radical form.​

Accepted Solution

[tex]c=3\sqrt{3}\\a=4\sqrt{2}[/tex]Step-by-step explanation:The trigonometric ratios will be used used for finding the values of given variableFor cWe have to use a ratio that has perpendicular and base in it. so we will use tan x[tex]tan\ 60 = \frac{P}{B}\\tan\ 60=\frac{c}{3}\\\sqrt{3}=\frac{c}{3}\\3*\sqrt{3}=c\\c=3\sqrt{3}[/tex]similarly for a[tex]sin\ 45 = \frac{b}{h}\\\frac{\sqrt{2}}{2}=\frac{a}{8}\\\frac{\sqrt{2}}{2}*8=a\\a=4\sqrt{2}[/tex]Hence,[tex]c=3\sqrt{3}\\a=4\sqrt{2}[/tex]Keywords: Triangles, Trigonometric RatiosLearn more about triangle at:brainly.com/question/10879401brainly.com/question/10940255#LearnwithBrainly