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Gutter Measurements

April 15th, 2010 |

Trigonometry math question?

When a truck with a tray behind the crosses over a stream and moves up one unit pronounced, you may be scratching the surface of the road. Suppose a truck and driveway entrance are measured. The base of the tray is 1 meter of the road, the road to the slopes of the stream to 10 degrees, the driveway to the slopes of the ditch at 15 degrees. What is the longest extension that truck may have to keep scraping the road. Take the length of the extension as measured from the final point above the rear axle (rear wheel). Thank you very much for all the help. By the way this question came with a diagram, but is poorly photocopied so I can not really see it. Thanks again!

………………………… , …….>'. ,> ………………….. ,…….. . >. … ,> …………….. , …………… ….. , …….> ……….. , ………………….. ……….. > ….. , …………………………. …… >. ………………………………… . ,. ………………………………. (…….) … ………………………….. ,(….._…….) <=== Front wheel ….. …………………. .. , ….(…..(_)…..) ……. …………… , ………… (_____) ……… …….. , ….. … Angle of the road = 10 SDRs, Ang. of Dvwy ,________|________________ SDR = 15 v ………. ……. <V V === …. V / V <==== <v === = This is the extension of the tray …. v <==== We have to find the length of the extension pan back so as not to scrape the road (I think you mean to type "no" instead of "no") is basically a triangle that looks like this …. in the extensions …. ………………………….. ………… ………………… ………………………. …… ………………………………. ……….. … ……………………………….. v ….. V. …__. v_ ……………………………… …. v … v. (…….) …………………………….. v v. …. ….(…..__….) ……………………… .. v ….. v. ……..(…..(…)…..) <=== Rear wheel ……….. …………. ….. v v. …………..(…..(__)….). ……………… v V. ….. ……………… (…………) ………….. V. V …. …….. …… ………….. —— / V. ………….. ………… … … Angle = 15 SDR road "is the v ………. more ,__________|_____ angle SDR's critical that the angle of the road …………. 10 …………………… …………. V. .. v ……………. ……………………….. V. …. …………………………… v …… v …. v …'…. <V == a right angle = 90 degrees …………………………….. v v. …… …. ……. v ……………………….. v v. ….. ………….. …'.. <V === side length = 1 m …………………… v ….. v. ……. …………………. …. vv ………………. v.. ………………… ………….. …. vv ………….. …….. v. ………………. …………… v v. ……… … ………….. v <== 15 SDR …………… vv ………. ,__________|_______________________ So … you know the length of the trangle side opposite the angle of 15 degrees is equal to the height "of the tray out of the earth "…… also know that the critical angle is the angle of the driveway … which is 15 degrees ….. Finally, we let "x" side of the triangle represent rectangle adjacent to the angle of 15 degrees …. What do you know about the trigonometric ratios as far as right triangles?? We know that "So / _ = O / A =" duration of OPP. adj side and duration. side "tan (angle) = O / A Tan (SDR 15) = 1 m / x Solving for" x " find that x = 1 m / (tan 15 SDRs) = 1 m / (0.268) = 3.73 m So this is telling us that the length of the tray may not exceed 3.73 m. … of other So when entering the driveway (located on a slope of 15 degrees), with the extension of the tray scraping the driveway …. So the maximum length the rear tray can be (and still do not scrape the driveway) is 3.73 m

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