Geometria 9.osztály

`1.`

`color(blue)(alpha+beta+gamma=180°)`

`3x+7x+8x=180°`

`18x=180°`

`x=10°`

`alpha=3*10°=color(red)(30°)`

`beta=7*10°=color(red)(70°)`

`gamma=8*10°=color(red)(80°)`

`2.`

`a=c-1` `cm`

`b=3` `cm`

`color(blue)(a^2+b^2=c^2)`

`(c-1)^2+3^2=c^2`

`c^2-2c+1+9=c^2`

`2c=10`

`c=color(red)(5)` `color(red)(cm)`

`a=color(red)(4)` `color(red)(cm)`

`3.`

`a=6` `cm`

`color(blue)(m=a/2sqrt(3)`

`m=6/2*sqrt(3)=color(red)(3sqrt(3)≈5.196` `color(red)(cm)`

A többit csak később tudom küldeni!

`4.`

`a=12` `cm`

`c=20` `cm`

Beírt kör:

`color(blue)(T=r*s)`

`b=sqrt(20^2-12^2)=16` `cm`

`T=(12*16)/2=96` `cm^2`

`s=(12+16+20)/2=24` `cm`

`r=96/24=color(red)(4)` `color(red)(cm)`

Köréírt kör:

`color(blue)(R=c/2)`

`R=20/2=color(red)(10)` `color(red)(cm)`

`5.`

`a=8` `cm`

`b=5` `cm`

`color(blue)((a/2)^2+m^2=b^2)`

`m=sqrt(5^2-(8/2)^2)=color(red)(3)` `color(red)(cm)`

`K=8+5+5=color(red)` `color(red)(cm)`

`T=(8*3)/3=color(red)(12)` `color(red)(cm^2)`

`6.`

`T=19.63` `cm^2`

`color(blue)(T=r^2pi)`

`19.63=r^2pi`

`r=sqrt((19.63)/pi)≈color(red)(2.5)` `color(red)(cm)`

`7.`

`r=8.7` `mm`

`color(blue)(K=2pir)`

`K=2pi*8.7≈color(red)(54.66)` `color(red)(mm)`