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Question-197670




Question Number 197670 by mr W last updated on 26/Sep/23
Commented by mr W last updated on 26/Sep/23
unsolved old question Q#197017
You can't use 'macro parameter character #' in math mode
Commented by ajfour last updated on 26/Sep/23
https://youtu.be/Y2LCMHAw3Fw?si=Vt7lXmpu1xLMVuB9
Commented by ajfour last updated on 26/Sep/23
A simple educational video i posted hours back, on dy/dx if y=x and if y= x^2
Commented by mr W last updated on 26/Sep/23
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Answered by mr W last updated on 26/Sep/23
Commented by mr W last updated on 26/Sep/23
s=side length of ΔABC  tan α=(s/3)×((√3)/2)×(1/(s−(s/3)×(1/2)))=((√3)/5)  a=(s/2)×tan α=(s/2)×((√3)/( 5))=((s(√3))/(10))  b=(s/2)  β=90°−60°=30°  c=b−2a cos β=(s/2)−2×((s(√3))/(10))×((√3)/2)=(s/5)  ((blue area)/(ΔABC))=((c/s))^2 =((1/5))^2 =(1/(25)) ✓
s=sidelengthofΔABCtanα=s3×32×1ss3×12=35a=s2×tanα=s2×35=s310b=s2β=90°60°=30°c=b2acosβ=s22×s310×32=s5blueareaΔABC=(cs)2=(15)2=125
Commented by mr W last updated on 26/Sep/23
you are right sir!  i took tan α wrongly as sin α.
youarerightsir!itooktanαwronglyassinα.
Commented by ajfour last updated on 26/Sep/23
triangle sides   6s  and  2c  ((6s)/2)×tan 30°=3stan α+(c/(cos 30°))  ..(i)  ((sin α)/(2s))=((sin (α+60°))/(6s))  ⇒  3sin α=(1/2)sin α+((√3)/2)cos α  ⇒  tan α=((√3)/5)  now   from  (i)  s(√3)=((3(√3))/5)s+((2c)/( (√3)))  (c/s)=(3/5)   ⇒   ((2c)/(6s))=(1/5)  r_(area) =(1/(25))
trianglesides6sand2c6s2×tan30°=3stanα+ccos30°..(i)sinα2s=sin(α+60°)6s3sinα=12sinα+32cosαtanα=35nowfrom(i)s3=335s+2c3cs=352c6s=15rarea=125

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