Answer:
Option B is correct 65°
Step-by-step explanation:
Apply the trigonometric identity sine
[tex]sin\ x=\frac{6.1}{6.7}\\\\sin\ x= 0.9104\\x=sin^{-1}(0.9104)\\x=65[/tex]
Do not forget to convert your calculator into degree form if it is set to radian.
Alright since you haven't studied trigonometry forget what i said here xD
The table given are the ratios of the respective angles 55, 65, 75.
First we need the adjacent side of the triangle. We have the opposite side of the triangle which is 6.1 and the hypotenuse which is 6.7 we use Pythagoras theorem
[tex]a^2+b^2=c^2\\a^2+(6.1)^2=(6.7)^2\\a^2=(6.7)^2-(6.1)^2\\a^2=7.68\\a=\sqrt{7.68}\\a=2.77 \\[/tex]
So now lets compare the ratios in table
Firstly
[tex]\frac{adjacent\ leg \ length}{hypotenuse\ leg \ length} = \frac{2.77}{6.7}=0.413\\\\\frac{opposite\ leg \ length}{hypotenuse\ leg \ length}=\frac{6.1}{6.7}=0.91 \\\\\frac{opposite\ leg \ length}{adjacent\ leg \ length}=\frac{6.1}{2.77}=2.2[/tex]
so we can see that all these values 0.413, 0.91, 2.2 correspond to the angle 65° so Option B is correct
