<p>A clock has a radius of 6 inches. What is the straight-line distance between the minute-hand of the clock from the times of 3:00 and 3:20?</p>
<p>Is the answer 6√2 ?
Let me know then explain if it’s right.</p>
<p>This is pretty tricky. First I am assuming that the minute hand has length equal to the radius (this should have been stated in the problem). Now, draw a circle with an equilateral triangle inscribed in it. The vertices of the triangle are at 0, 20 and 40 minutes. Also draw 3 radii to each vertex. This splits the triangle into 3 congrient triangles. Let’s just look at the one with the side we are looking for (the right-most triangle). Note that this triangle has angles of measure 30, 30, and 120 (if you need more explanation as to why, let me know). Draw an altitude from the vertex at the center of the circle to the segment we are looking for. This splits the triangle into two 30, 60, 90 triangles. The hypotenuse is the radius of the circle, with length 6. So the side opposite 60 is 3sqrt(2). This is half the length we’re looking for. So the answer is 6sqrt(2).</p>
<p>Thanks for your effort. I was going to right this :D</p>
<p>@DrSteve, wouldn’t it be 6sqrt(3)? 30-60-90 triangles have lengths in the ratio 1:sqrt(3):2.</p>
<p>@rspence</p>
<p>Of course it would :)</p>
<p>Looks like I made a typo. Please replace both instances of my sqrt(2) by sqrt(3) in my last post.</p>
<p>Nice catch.</p>