(a) Prove that a triangle with sides 3, 7, 8 contains a 60 degree
  angle.<br />

  <p>(b) Three points A, B and C lie in this order on a line, and P
  is any point in the plane. Use the Cosine Rule to prove that:</p>
  



 
      


<br clear="all" /><table border="0" width="100%"><tr><td>
<table align="center"><tr><td nowrap="nowrap" align="center">
</td><td nowrap="nowrap" align="center">
<i>AP</i><sup>2</sup><hr noshade="noshade" size="1" /><i>AB</i>.<i>AC</i><br /></td><td nowrap="nowrap" align="center">
+</td><td nowrap="nowrap" align="center">
<i>CP</i><sup>2</sup><hr noshade="noshade" size="1" /><i>CA</i>.<i>CB</i><br /></td><td nowrap="nowrap" align="center">
 = 1 + </td><td nowrap="nowrap" align="center">
<i>PB</i><sup>2</sup><hr noshade="noshade" size="1" /><i>BA</i>.<i>BC</i><br /></td><td nowrap="nowrap" align="center">
.</td></tr></table>
</td></tr></table>




    

  <p><img alt="Triangle." src=
  "/content/01/02/15plus3/triangle.gif" /></p><br />