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Question-213436




Question Number 213436 by mr W last updated on 05/Nov/24
Answered by A5T last updated on 05/Nov/24
Commented by mr W last updated on 05/Nov/24
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Commented by A5T last updated on 05/Nov/24
sinθ=((15)/( (√(26^2 +15^2 ))))=((15)/( (√(901))))⇒cosθ=((26)/( (√(901))))  ⇒sin2θ=2sinθcosθ=((780)/(901))  [ABC]=15(((26×2+25×2+2x)/2))=(((26+x)(26+25)sin2θ)/2)  ⇒x=27
sinθ=15262+152=15901cosθ=26901sin2θ=2sinθcosθ=780901[ABC]=15(26×2+25×2+2x2)=(26+x)(26+25)sin2θ2x=27
Answered by mr W last updated on 05/Nov/24
Commented by mr W last updated on 05/Nov/24
tan α=((15)/x)  tan β=((15)/(26))  tan γ=((15)/(25))  α+β+γ=((180°)/2)=90°  tan α=(1/(tan (β+γ)))=((1−tan β tan γ)/(tan β+tan γ))  ((15)/x)=((1−((15)/(26))×((15)/(25)))/(((15)/(26))+((15)/(25))))=((26×25−15^2 )/(15×(25+26)))=(5/9)  ⇒x=27  A=(25+26+27)×15=1170
tanα=15xtanβ=1526tanγ=1525α+β+γ=180°2=90°tanα=1tan(β+γ)=1tanβtanγtanβ+tanγ15x=11526×15251526+1525=26×2515215×(25+26)=59x=27A=(25+26+27)×15=1170

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