+0  
 
0
53
1
avatar

In a triangle, the degree measure of one angle is 60 more than that of anohter.  The ratio of the lengths of the sides opposite these two angles is 2:1.  Fidn the degree-measure of the largest angle of this triangle.

 Dec 17, 2019
 #1
avatar+106519 
+1

Let the meaure  of  the smaller angle   = A

And the measure of the  other known angle  be  A+ 60

 

And by the Law  of Sines

 

sin (A + 60)               2          

_________  =         ___         so we have

  sin A                        1

 

sinAcos60  + sin60cosA

___________________     =      2

           sin A

 

sinA  + √3cosA

_____________       =   2

          2sin A

 

sinA              (√3/2) cot A   =   2

______  +  

2sinA

 

 

(1/2)  +  (√3/2)cot A  =  2

 

(√3/2)cotA  = 3/2

 

cot A  = 3 / √3

 

cot A  =   √3

 

arccot(√3)  = A  =    30°

 

So  the second known angle  =  A + 60   =  90°.....and this must be the measure of the largest angle in the triangle

 

 

cool cool cool

 Dec 17, 2019

4 Online Users

avatar