Answer:
sinE = 1/2
(which also means the angle E is 30°)
Step-by-step explanation:
sine = opposite/hypotenuse
so we first need to solve for the side opposite angle E using the pythagorean theorem
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex](8\sqrt{21})^{2} + b^{2} = (16\sqrt{7})^{2}[/tex]
[tex]64(21) + b^{2} = 256(7)\\[/tex]
[tex]1344 + b^{2} = 1792[/tex]
[tex]b^{2} = 448[/tex]
[tex]b = \sqrt{64 * 7}[/tex]
[tex]b = 8\sqrt{7}[/tex]
then plug into the sine formula
sine = opposite/hypotenuse
sinE = [tex]8\sqrt{7}[/tex] / [tex]16\sqrt{7}[/tex] = 1/2
(which also means the angle E is 30°)
