document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198890>Question 1198890</A>: <I><SPAN STYLE=\"word-break: break-all;\"> VABC is a right pyramid whose base is an equilateral triangle Abc of side 8cm. If VA = 13cm and the altitude of DABC meet at x. Calculate <BR>\n" );
document.write( "AX, VX, the angle which VAB makes with ABC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848221 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Height of the Equilateral Triangle Base (Altitude)**\r<BR>\n" );
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document.write( "* In an equilateral triangle, the altitude bisects the base.<BR>\n" );
document.write( "* Let the altitude of the equilateral triangle be 'h'.<BR>\n" );
document.write( "* Using the Pythagorean theorem in one of the right-angled triangles formed by the altitude:<BR>\n" );
document.write( "   (h)² + (4)² = (8)² <BR>\n" );
document.write( "   h² = 64 - 16 = 48<BR>\n" );
document.write( "   h = √48 = 4√3 cm\r<BR>\n" );
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document.write( "**2. Find the Height of the Pyramid (VX)**\r<BR>\n" );
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document.write( "* Consider the right triangle VAX, where VX is the height of the pyramid.<BR>\n" );
document.write( "* Using the Pythagorean theorem:<BR>\n" );
document.write( "   (VX)² + (AX)² = (VA)²<BR>\n" );
document.write( "   VX² + (4√3)² = (13)² <BR>\n" );
document.write( "   VX² + 48 = 169<BR>\n" );
document.write( "   VX² = 121<BR>\n" );
document.write( "   VX = 11 cm\r<BR>\n" );
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document.write( "**3. Find AX**\r<BR>\n" );
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document.write( "* From the previous step, we found that AX = 4√3 cm.\r<BR>\n" );
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document.write( "**4. Find the Angle VAB**\r<BR>\n" );
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document.write( "* Consider the right triangle VAX.<BR>\n" );
document.write( "* Let the angle VAB be θ.<BR>\n" );
document.write( "* cos(θ) = AX / VA <BR>\n" );
document.write( "* cos(θ) = (4√3) / 13<BR>\n" );
document.write( "* θ = arccos((4√3) / 13) <BR>\n" );
document.write( "* θ ≈ 49.11 degrees\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **AX = 4√3 cm**<BR>\n" );
document.write( "* **VX = 11 cm**<BR>\n" );
document.write( "* **Angle VAB ≈ 49.11 degrees**<BR>\n" );
document.write( " </SPAN>\n" );
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