Question 1207162
.
the arch of this bridge is an arc of a circle. the arc measures 80 degrees 
and the bridge spans a 200 meters across a valley. 
what is the length of the bridge's arch?
~~~~~~~~~~~~~~~~~~~~~~


<pre>
Make a sketch.

You have an arc with the center O, the central angle of 80 degrees and the endpoints A and B
that are endpoint of the bridge.

Draw the radius from O, which bisects the arc and intersect the horizontal chord 
at point C.


You have right-angled triangle AOC with one acute angle of 40 degrees and the opposite leg 
AC of 200/2 = 100 meters long and adjacent leg OC.


The radius of the arc is  R = {{{(AC)/sin(40^o)}}} = {{{100/0.6427}}} = 155.5936 m  (rounded).


The length of the bridge is the length of the arc AB and is equal to 

    {{{R*theta}}} = {{{155.5936*(2*pi*(80/360))}}} = {{{155.5936*(2*3.14159*(80/360))}}} = 217.25 m (rounded).


<U>ANSWER</U>.  The length of the bridge is about 217.25 meters.
</pre>

Solved.


===============


The solution in the post by &nbsp;@MathLover1 is &nbsp;INCORRECT.