In this case we know the three sides of the triangle, then this is a SSS triangle (Side Side Side). To solve this case, first we must use the Law of Cosines, applied to the opposite side to the angle we want to find. We want to find angle W, and its opposite side is XV, then we apply the Law of Cosines to the side XV: XV^2=XW^2+WV^2-2(XW)(WV)cos W Replacing the known values: 116^2=96^2+89^2-2(96)(89)cos W Solving for W 13,456=9,216+7,921-17,088 cos W 13,456=17,137-17,088 cos W 13,456-17,137=17,137-17,088 cos W-17,137 -3,681=-17,088 cos W (-3,681)/(-17,088)=(-17,088 cos W)/(-17,088) 0.215414326=cos W cos W = 0.215414326
Solving for W: W= cos^(-1) 0.215414326 Using the calculator: W=77.56016397° Rounded to one decimal place: W=77.6°
Example: these two triangles are similar: If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°. So AA could also be called AAA (because when two angles are equal, all three angles must be equal)
You solve this by plugging one equation into the other. Usually you have to rewrite one equation to make this work. In this case I choose to rewrite y-4x=0 as y=4x.
After plugging it into the second, you get:
3x + 6*4x = 9 => 27x = 9 => x=1/3
Putting this solution back into y=4x gives us y=4/3
