The rectangular front windshield of the bus has the length of 1.5√3 m and the width of 1.5 m . The wipers are attached to the bottom corners. If the length of each wiper is equal to the width of the windshield, find the percentage of the windshield that wipers can reach. (Solve this task without using Trigonometry)
Answers
Explanation:
Area covered by wiper-area of arc(AOD) +area of traingleAOB+area of arc(BOC)
We know AO and OB are wipers,whose lengths are 1.5
In AABC
AB^2+BC^2=AC^2
➡(1.5-√3)^2+(1.5)^2=(AC)^2
➡2.25×3+2.25=(AC)^2
➡2.25×4=AC^2
➡AC-3
Also AO=1.5
similarly using Pythagoras theorem in AOBC
we get,
OC=1.5
this shows that point O is the bisector of diagonal AC
so,AO=OC
also from property of rectangle we know that, diagonal bisects each other equally so,O will also be the bisector of diagonal
BD
hence OB=OD=1.5
AC-BD (property of triangle) AC/2=BD/2
OB-OC,hence
OB=OC-OD=OA=1.5=AD=BC
69
Hence OAD will be an equilateral triangle
SO,
angle OAD=60
similarly angleOBC=60
➡area of sector-angle of that sector xarea of circle/360
area of arc(AOD)+arc(BOC)=60/360 x3.14 x1.5x1.5 +60/360 x3.14x1.5x1.5
=2×(60/360)x1.5x1.5
area of triangleAOB=area of rectangle/4
(diagonal divides the rectangle in 4 equal parts)
area of triangle=1.5x1.5√3/4
=>1.5x2.6/4-3.90/4
-0.975 or 0.98(approx)
Area covered by wiper=.98+2×60/360 x3.14x1.5x1.5
=.98+0.75×3.14-2.35+0.97
= 2.35+.98
➡Percentage of area of windshield covered by wiper-3.3×100/3.9-=84.61
➡hence percentage of area of windshield covered by wiper is 85percent(approx)
