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

Try calculation via our triangle calculator.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
See also our right triangle calculator.
Do you know the volume and unit volume, and want to convert volume units?
Do you want to convert time units like minutes to seconds?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: