Answer:
48
Step-by-step explanation:
We are going to use trigonometry to solve for the wanted angle
Remember these are the trigonometric functions
( Remember SOH CAH TOA )
Sine = Opposite over Hypotenuse (SOH)
Cosine = Adjacent over Hypotenuse (CAH)
Tangent = Opposite over Adjacent (TOA)
For angle Ф
we are given its adjacent side length (6) and the hypotenuse (9)
Adjacent and hypotenuse corresponds with the trig function Cosine
So we will use cosine to solve for the missing angle
( let x = missing angle )
( remember cosine = adjacent over hypotenuse )
[tex]cosX=\frac{6}{9} \\\frac{6}{9} =.66\\cos(x)=.66[/tex]
now we want to get rid of the "cos" on the x
To do so we take the inverse of cos ( arc cos ^-!1 ) and apply it to each side
so...
[tex]arcos(cos(x))=x\\arccos(.66)=48.1[/tex]
we're left with x = 48.1
