Step-by-step explanation:
remember the law of cosine (I call it the general law of Pythagoras) :
c² = a² + b² - 2ab×cos(C)
c is the side opposite of C, a and b are the other 2 sides.
that applies to all sides of a triangle. we only need to make sure to use an opposite pair of side and angle, abd then the other 2 sides.
in our case, I assume e, f, g are the 3 sides, and E, F, G are the corresponding opposite angles.
we are missing f and get
f² = e² + g² - 2eg×cos(46) = 64 + 2.56 - 2×8×1.6×cos(46) =
= 66.56 - 17.78325428... = 48.77674572...
f = 6.98403506...
so, now to find E, we have
e² = g² + f² - 2gf×cos(E)
e² - g² - f² = -2gf×cos(E)
(e² - g² - f²)/-2gf = cos(E)
(64 - 2.56 - 48.77674572...)/-(2×1.6×6.98403506...) = cos(E)
cos(E) = -0.566616137...
E = 124.5145941...° ≈ 124.5°
