Question 1096676
NOTE:
I assume this is math homework,
and not physics homework.
I also assume that the answer is expected to be a length in feet,
because if the expected answer was 1.9%,
There would be no need to know the radius.
In that case, you would compare the length of
a {{{19^o}}} arc on a unit circle with 
(the measure of the arc in radians)
to the sine of {{{19^o}}} ,
to find that
{{{(19*pi/180)/sin(19^o)=about1.0185657}}}
 
A PICTURE AND THEN AN ANSWER IN 1,000 WORDS:
{{{drawing(300,300,-45,45,-45,45,
circle(0,0,1),circle(0,0,43),
green(triangle(0,0,40.66,0,40.66,14)),
green(rectangle(40.66,0,37.66,3)),
triangle(0,0,40.66,14,40.66,-14),
red(arc(0,0,30,30,-19,0)),
red(arc(0,0,34,34,0,19)),
locate(16,7,19^o),locate(18,0,19^o)
)}}}
 
LENGTH OF THE ARC:
Using radians:
The angle measure {{{38^o}}} is {{{(38^o/180^o)*pi}}} in radians.
The length of an arc of that measure is
angle in radians times radius.
For a circle of {{{43ft}}} radius, it is {{{19*43pi/90}}} .
Without radians:
The whole circumference is {{{2*pi*43ft}}} .
The arc is a fraction of that. It is {{{38^o/360^o=19/180}}} .
So, the arc length is {{{(19/180)*2*pi*43ft=19*43*pi/90}}}{{{ft}}} .
That is approximately {{{28.5187ft}}} .
 
LENGTH OF THE CHORD:
Connecting the ends of the chord to the center of the circle,
you form an isosceles triangle. 
It has two legs measuring {{{43ft}}} forming an angle measuring {{{38^o}}} .
It's base is the chord, whose length {{{x}}} we need to find
If Law of cosines was taught in class, you may be expected to use it.
{{{chord^2=(43ft)^2+(43ft)^2-2*(43ft)*(43ft)*cos(38^o)=(2-2cos(38^o))*(43ft)^2}}} .
So, {{{chord=sqrt(2-2cod(38^o))*(43ft)}}}
That is approximately {{{27.9989ft}}} .
 
Otherwise, you could split that triangle into two right triangles,
and use trigonometry to find the length of half the chord as
{{{sin(19^o)*(43ft)=approximately13.99943ft}}} ,
so the length of the chord is twice that,
or approximately {{{27.9989ft}}} .
 
By how much does the arc exceed the chord?
We calculate the difference as about {{{28.5187ft-27.9989ft=0.5198ft}}} ,
So, I would answer {{{highlight(0.52ft)}}} .