Explanation:
remember, the sum of all angles in a triangle is 180°.
and then remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides of the triangle, A, B, C are the corresponding opposite angles for the sides.
the third angle (opposite of a) is
180 - 90 - 76°49' = 90 - 76 49/60° =
= 90 - 76.81666666...° = 13.18333333...°
as 1 degree = 60 arc minutes.
and so,
a/sin(13.18333333...) = 42.42/sin(76.81666666...)
a = 42.42×sin(13.18333333...)/sin(76.81666666...) =
= 9.936503757... ≈ 9.94 km