SOLUTION: The world's longest covered bridge crosses the Saint John River in Hartland, New Brunswick. From two points, X and Y, 100m apart on the same side of the river, the lines of sight t

Algebra ->  Trigonometry-basics -> SOLUTION: The world's longest covered bridge crosses the Saint John River in Hartland, New Brunswick. From two points, X and Y, 100m apart on the same side of the river, the lines of sight t      Log On


   

Question 1064024: The world's longest covered bridge crosses the Saint John River in Hartland, New Brunswick. From two points, X and Y, 100m apart on the same side of the river, the lines of sight to the far end of the bridge, Z, make angles of 85.6 degrees and 79.8 degrees with the river bank, as shown. What is the length of the bridge, b, to the nearest 10 m?
This is not making any sense to me...thank you for your help!

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


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%2F%28AX%29%22%22=%22%22tan%28%2285.6%B0%22%29           AB%2F%28AY%29%22%22=%22%22tan%28%2279.8%B0%22%29    

AB%22%22=%22%22AX%2Atan%28%2285.6%B0%22%29          AB%22%22=%22%22AY%2Atan%28%2279.8%B0%22%29 

AB%2Ftan%28%2285.6%B0%22%29%22%22=%22%22AX         AB%2Ftan%28%2279.8%B0%22%29%22%22=%22%22AY

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

AX + AY = 100, so 

AB%2Ftan%28%2285.6%B0%22%29%22%22%2B%22%22AB%2Ftan%28%2279.8%B0%22%29%22%22=%22%22100

Factor out AB on the left:



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



Solve for AB





Rounding that to the nearest 10 meters, we get

390 meters.

If you go to this site,

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

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

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

Edwin