Hypotenuse 64694

Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the content of triangle ABC if the line on the hypotenuse is 0.2 dm long and if | ∢ACS | = 30 °.

Correct answer:

S =  3.4641 cm2

Step-by-step explanation:

t=0.2 dm cm=0.2 10  cm=2 cm ACS=30  SCB=90ACS=9030=60   sinαsinACS=tc/2 sinβsinSCB=tc/2 β=90°α  sinαsinACS=sin(90°α)sinSCB sinACS sin(90°α)=sinSCB sinα sin(αβ)=sinα.cosβcosα.sinβ  sinACS (sin90°cosαcos90°sinα)=sinSCB sinα sinACS cosα=sinSCB sinα sinACS/sinSCB=sinα/cosα tanα=sinACS/sinSCB  α=π180°arctan(sinACS/sinSCB)=π180°arctan(sin30° /sin60° )=π180°arctan(0.5/0.866025)=30 β=90α=9030=60   c=2 t sinαsinACS=2 t sin30° sin30° =2 2 sin30° sin30° =2 2 0.50.5=4 cm  a=c sinα=c sin30° =4 sin30° =4 0.5=2 cm b=c sinβ=c sin60° =4 sin60° =4 0.866025=3.4641 cm  S=2a b=22 3.4641=2 3=3.4641 cm2

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