document.write( "Question 1191760: Cj needs to know the width of a river. He climbs a tree 10 meters high above the ground and finds that the angle of depression of the two opposite banks of the river is 40° and 15°, respectively. How wide is the river? \n" ); document.write( "
Algebra.Com's Answer #823589 by ankor@dixie-net.com(22740)\"\" \"About 
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Cj needs to know the width of a river.
\n" ); document.write( " He climbs a tree 10 meters high above the ground and finds that the angle of depression of the two opposite banks of the river is 40° and 15°, respectively.
\n" ); document.write( " How wide is the river?
\n" ); document.write( ":
\n" ); document.write( "One way to do this is to solve two right triangles.
\n" ); document.write( "The larger triangle is formed by top of the tree and the distance from the base of the tree to the furthest bank.
\n" ); document.write( "The angle of depression of 15 degrees, gives an interior angle of 75 at the top of the tree. (90-15)
\n" ); document.write( "the distance(a)from the tree to the far river bank is the side opposite
\n" ); document.write( "the tree is the side adjacent
\n" ); document.write( "tan(75) = \"a%2F10%29\"
\n" ); document.write( "a = tan(75) * 10
\n" ); document.write( "a = 37.32 meters
\n" ); document.write( ":
\n" ); document.write( "The smaller triangle is formed by top of the tree and the distance from the base of the tree to the nearest bank.
\n" ); document.write( "The angle of depression of 40 degrees, gives an interior angle of 50 at the top of the tree.(90-40)
\n" ); document.write( "the distance (b) from the tree to the near river bank is the side opposite
\n" ); document.write( "the tree is the side adjacent
\n" ); document.write( "tan(50) = \"b%2F10%29\"
\n" ); document.write( "b = tan(50) * 10
\n" ); document.write( "b = 11.92 meters
\n" ); document.write( ":
\n" ); document.write( "The width of the river then is: 37.32 - 11.92 = 25.4 meters \n" ); document.write( "
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