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    sin α sin ACS =  tc/2   sin β sin SCB =  tc/2  β = 90°  α   sin α sin ACS =  sin (90°  α) sin SCB  sin ACS   sin (90°  α)  = sin SCB   sin α  sin (α  β) = sin α.cos β  cos α.sin β   sin ACS   ( sin 90° cos α  cos 90° sin α)  = sin SCB   sin α  sin ACS   cos α   = sin SCB   sin α  sin ACS / sin SCB   =  sin α  / cos α  tan α =  sin ACS / sin SCB  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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