Question 1064024
<pre>
{{{drawing(800,1600/7,-10,410,-80,40,
locate(-6,33,X),locate(-6,-65,Y),locate(-6,5,A),locate(393,5,B),
locate(3,27,"85.6°"), locate(3,-58,"79.8°"),rectangle(0,0,4,4),
locate(90,0,matrix(1,3,HARTLAND,COVERED,BRIDGE)),
line(0,0,389.296),triangle(0,29.9547,0,-70.0453,389.296,0),line(0,-70.0453,0,29.9547) )}}}

The bridge is AB.  The points X and Y are on the side of the
river.  X and Y are on opposite sides of A. 

{{{AB/(AX)}}}{{{""=""}}}{{{tan("85.6°")}}}           {{{AB/(AY)}}}{{{""=""}}}{{{tan("79.8°")}}}    

{{{AB}}}{{{""=""}}}{{{AX*tan("85.6°")}}}          {{{AB}}}{{{""=""}}}{{{AY*tan("79.8°")}}} 

{{{AB/tan("85.6°")}}}{{{""=""}}}{{{AX}}}         {{{AB/tan("79.8°")}}}{{{""=""}}}{{{AY}}}

We are given that XY = 100m, and XY = AX + AY, so

AX + AY = 100, so 

{{{AB/tan("85.6°")}}}{{{""+""}}}{{{AB/tan("79.8°")}}}{{{""=""}}}{{{100}}}

Factor out AB on the left:

{{{matrix(1,5,

AB*(matrix(1,3,1/tan("85.6°"),""+"",1/tan("79.8°"))),
"",
""="",
"",
100)}}}

Get a calculator and calculate the expression in the parentheses
on the left side.

{{{matrix(1,5,

AB*(0.2568742058),
"",
""="",
"",
100)}}}

Solve for AB

{{{matrix(1,5,

AB,
"",
""="",
"",
100/(0.2568742058))}}}

{{{matrix(1,5,

AB,
"",
""="",
"",
389.2956075)}}}

Rounding that to the nearest 10 meters, we get

390 meters.

If you go to this site,<font size=1>

http://www.tourismnewbrunswick.ca/Products/H/Hartland-Covered-Bridge-National-Historic-Site.aspx</font>

you'll see pictures of the bridge and read this:

"This 390-m (1,282-ft.) bridge officially opened on July 4, 1901,..."

Edwin</pre>