Jump to content
Sign in to follow this  
jonathanwoenardi

Berapakah luas segitiga ABC ?

Recommended Posts

Soal ini menarik sial.


 



Dipunyai sistem persamaan


$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$


$$\frac{abc}{\sin A \sin B \sin C}=1000000$$


Maka $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=100$ dan


$$S=\frac{1}{2}ab \sin C=\frac{abc}{2}\cdot \frac{\sin C}{c}=500 \cdot \frac{1}{100}=5.$$



Edited by donjar
  • Upvote 1

Share this post


Link to post
Share on other sites

Soal ini menarik sial.

 

Dipunyai sistem persamaan

$$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$

$$\frac{abc}{\sin A \sin B \sin C}=1000000$$

Maka $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=100$ dan

$$S=\frac{1}{2}ab \sin C=\frac{abc}{2}\cdot \frac{\sin C}{c}=500 \cdot \frac{1}{100}=5.$$

kalo ane caranya beda gan

misalnya luas segitiga x

Maka 2x = ab sin C = bc sin A = ac sin B

Kalikan didapat 8x^3 = (abc)^2.sinA.sinB.sinC

8x^3 = 1000^2 * 1/1000

8x^3 = 1000

x^3 = 125

x = 5

Sorry ngak bisa latex, maklum newbie + mobile (pake iPad).

Saran : maunya ada editor latex di setiap post editor (pas reply)

Share this post


Link to post
Share on other sites

sin A/a = sin B/b = sin C/c

sehingga

sin^3 A/a^3 = 1/100^3

sin A/a = 1/100

kemudian...

Luas segitiga^3 = 1/8. Sin a sin b sin c . a^2. b^2. c^2

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this  

×