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Find the area of triangle ABC.

 

Given: angle A = 2 * angle C, AB = 36, BC = 60.

 

This is a really hard problem!

 Dec 16, 2023
 #1
avatar+129316 
+1

                  A

 

        36

 

B            60                   C

 

Law of Sines :

 

sin A / 60  =  sin C / 36

 

sin A  / sin C  =   60  /  36

 

sin (2C) / sin C =  5 / 3

 

[ 2sin C cos C] / sin C  =  5/3

 

2cosC =  5/3       divide both sides by 2

 

cosC  =  5/6

 

arccos (5/6) = C ≈ 33.56°

 

A = 2C  ≈  67.12°

 

Angle B ≈  180  - 67.12 - 33.56   ≈  79.32°

 

approx area =  (1/2)(BC)(BA) sin (B)  =  (1/2) (60)(36)sin(79.32)  ≈  1061.3 units^2

 

cool cool cool

 Dec 16, 2023
edited by CPhill  Dec 16, 2023

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