Explanation:
first of all, remember, the sum of all angles in a triangle is always 180°.
so, we know all 3 angles :
90°
53°
180 - 90 - 53 = 37°
and now we use the law of sine to get the other side lengths.
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides.
A, B, C are the corresponding opposite angles.
so, we have here
126/sin(37) = b/sin(53) = c/sin(90) = c
that means the long side (opposite of the 90° angle) is c and is
c = 126/sin(37) = 209.3666578... m
and from
b/sin(53) = c
we get
b = c×sin(53) = 167.2076475... m
we need as much fence as the sum of all 3 sides (perimeter) :
126 + 167.2076475... + 209.3666578... = 502.5743053... m
one meter costs £1.24
so, the complete fence costs
so, the complete fence costs1.24 × 502.5743053... = £623.1921386... ≈ £623
in my opinion it would be better to round up to the next pound to cover the extra fraction of a meter and to have some wiggle room for some error.
that would mean then £624. but that's not what the problem text is asking for.