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lammy.

by lammy. at May 18, 2010

P, A , B, C are four points, in order, on a straight road that runs up a hillside and makes a constant angle of 10 degree with the horizontal.  A flagpole whose height is h m stands at P.  From A and B, the top of the flagpole has elevations of 30 degree and 5 degree respectively above the horizontal.  If AB is 100 m long, what is the height of the flagpole?  If Bc is also 100 m long, what is the elevation of the top of the flagpole from C ?

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(100/sin25)=(x/sin5) x=20.62280565 (20.62280565/sin80)=(y/sin30) y=10.47 height of flagpole (20.62280565/sin5)=(z/sin150) z=118.3100792 Law of Cosines c^2=a^2+b^2-2abcosC c^2=(118.31)^2+(100)^2-2(118.31)(100)cos175 c^2=47.569.21515 c=218.1036796 Now back to Law of Sines (218.1036796/sin175)=(118.3100792/sin(#)) sin(#)=0.0472774964 (#)theta=sin^-1(0.0472774964) (3)theta=2.7 degrees
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Allison082 Allison082 May 20, 2010

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