Question-209590

Question Number 209590 by SonGoku last updated on 15/Jul/24

Commented by SonGoku last updated on 15/Jul/24

$$\mathrm{Help}\:-\:\mathrm{me}! \\ $$

Answered by mr W last updated on 16/Jul/24

(A_(Δbig) /A_(Δsmall) )=(((1+20)×(0.85+17))/(1×0.85)) A_(Δsmall) =((√((1+0.85+1.095)(−1+0.85+1.095)(1−0.85+1.095)(1+0.85−1.095)))/4) A_(Δbig) =(((1+20)×(0.85+17))/(1×0.85))×((√((1+0.85+1.095)(−1+0.85+1.095)(1−0.85+1.095)(1+0.85−1.095)))/4) ≈178.318 or cos θ=((1^2 +0.85^2 −1.095^2 )/(2×1×0.85))=0.307926 sin θ=(√(1−0.307926^2 ))=0.951410 A_(Δbig) =(((1+20)×(0.85+17)×sin θ)/2) ≈178.318

$$\frac{{A}_{\Delta{big}} }{{A}_{\Delta{small}} }=\frac{\left(\mathrm{1}+\mathrm{20}\right)×\left(\mathrm{0}.\mathrm{85}+\mathrm{17}\right)}{\mathrm{1}×\mathrm{0}.\mathrm{85}} \\ $$$${A}_{\Delta{small}} =\frac{\sqrt{\left(\mathrm{1}+\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(−\mathrm{1}+\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(\mathrm{1}−\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(\mathrm{1}+\mathrm{0}.\mathrm{85}−\mathrm{1}.\mathrm{095}\right)}}{\mathrm{4}} \\ $$$${A}_{\Delta{big}} =\frac{\left(\mathrm{1}+\mathrm{20}\right)×\left(\mathrm{0}.\mathrm{85}+\mathrm{17}\right)}{\mathrm{1}×\mathrm{0}.\mathrm{85}}×\frac{\sqrt{\left(\mathrm{1}+\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(−\mathrm{1}+\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(\mathrm{1}−\mathrm{0}.\mathrm{85}+\mathrm{1}.\mathrm{095}\right)\left(\mathrm{1}+\mathrm{0}.\mathrm{85}−\mathrm{1}.\mathrm{095}\right)}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\approx\mathrm{178}.\mathrm{318} \\ $$$${or} \\ $$$$\mathrm{cos}\:\theta=\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{0}.\mathrm{85}^{\mathrm{2}} −\mathrm{1}.\mathrm{095}^{\mathrm{2}} }{\mathrm{2}×\mathrm{1}×\mathrm{0}.\mathrm{85}}=\mathrm{0}.\mathrm{307926} \\ $$$$\mathrm{sin}\:\theta=\sqrt{\mathrm{1}−\mathrm{0}.\mathrm{307926}^{\mathrm{2}} }=\mathrm{0}.\mathrm{951410} \\ $$$${A}_{\Delta{big}} =\frac{\left(\mathrm{1}+\mathrm{20}\right)×\left(\mathrm{0}.\mathrm{85}+\mathrm{17}\right)×\mathrm{sin}\:\theta}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\approx\mathrm{178}.\mathrm{318} \\ $$

Commented by SonGoku last updated on 16/Jul/24

$$\mathrm{Thank}\:\mathrm{you} \\ $$

Commented by maths_plus last updated on 16/Jul/24

$$\mathrm{cool} \\ $$

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