Answer:
The angle C measures 48.89°.
Step-by-step explanation:
We use the Sine inverse trigonometric function to solve for C.
In a triangle the ratio of the side opposite to angle C, and the hypotenuse is given by the Sine function:
[tex]sin(C)=\frac{opposite}{hypotenuse}[/tex]
and for our angle C, the opposite is 55 and the hypotenuse is 73; thus
[tex]sin(C)=\frac{opposite}{hypotenuse}=\frac{55}{73}=0.7534[/tex]
Now the inverse sine function gives back the angle C, if the ratio [tex]\frac{opposite}{hypotenuse}[/tex] is known, that is
[tex]\angle C=sin^{-1}(\frac{opposite}{hypotenuse})[/tex]
We know that for angle C
[tex]\frac{opposite}{hypotenuse}=0.7534[/tex]
therefore
[tex]\angle C=sin^{-1}(\frac{opposite}{hypotenuse})= sin^{-1}(0.7534})=48.89^o.[/tex]
[tex]\boxed{\therefore \angle C=48.89^o.}[/tex]
Note that we did not use an equation when evaluating [tex] sin^{-1}(0.7534)[/tex] that is because there isn't any: you have just got to use a calculator or memorize some values for the inverse sine function.
