<PRE><B>Question 1119202</B>
&lt;br&gt;
I don&#39;t see that it is possible to answer part a.  There are no parts of the wheel that are chords.  Each of the wheel spokes is a radius, but there are no chords.&lt;br&gt;
As for the angles, it APPEARS that there are 12 spokes making congruent 30 degree central angles; but there is nothing in the statement of the problem that tells us so.&lt;br&gt;
part b:  If r is the radius, then
{{{r/45 = tan(20)}}}
{{{r = 45*tan(20) = 16.38}}} approximately&lt;br&gt;
With the given measurements, we can also calculate the radius with
{{{r/48 = sin(20)}}}
{{{r = 48*sin(20) = 16.42 }}} approximately&lt;br&gt;
So the given measurements are consistent only to 1 or 2 decimal places.  So let&#39;s call the radius 16.4 inches.&lt;br&gt;
part c:  If the arc AB is increased from 70 to 72 degrees, then the angle the handle makes with the ground is changed to 18 degrees, so the contents will remain on the cart.  And since the handle doesn&#39;t change length, the end of the handle will no longer touch the ground.&lt;br&gt;
In the original configuration, the angle the bed of the cart makes with the ground is 20 degrees and the radius of the wheel is 16.4 inches.  When someone lifts the handle of the cart off the ground, the maximum height he can raise the handle, in order to keep the angle the bed makes with the ground at most 20 degrees, is twice the radius, or 32.8 inches.&lt;br&gt;
So if the pioneer lifts the handle to 48 inches above the ground, the contents of the cart will spill out long before he gets the handle to that height.</PRE>