Answer:
a = 3.46 , c = 9.9
Step-by-step explanation:
These are the following identities:
[tex]sinx=\frac{perpendicular}{hypotenuse} \\\\cosx=\frac{base}{hypotenuse}\\\\tanx=\frac{perpendicular}{base}\\[/tex]
Easier way to learn this is
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Sinx = per/hyp cosx = base/hyp tanx = per/base
So if use the angle 60° we can see that the opposite side(perpendicular) to the angle is 6 and the base side is a so we need the identity which uses the opposite side(perpendicular side) and the base side and not the hypotenuse so that is tan x so,
[tex]tan\ 60=\frac{6}{a} \\\\1.732=\frac{6}{a}\\\\1.732a=6\\a=\frac{6}{1.732}\\\\a=3.46\\[/tex]
So a = 3.46
Now to calculate c:
If we take the angle 45° and see the opposite side(perpendicular side) is 7 and the hypotenuse is c so need the identity which uses the opposite side(perpendicular side) and the hypotenuse and not the base, which is sin x so,
[tex]sin 45=\frac{7}{c}\\\\0.707=\frac{7}{c}\\\\0.707c=7\\\\c=\frac{7}{0.707}\\\\c =9.9\\[/tex]
so c = 9.9
