+0  
 
0
1092
5
avatar

Two sides and an angle are given. Determine whether the given information results in 1 triangle, 2 triangles, or none at all. a=7 b=9 B=49

Guest May 5, 2015

Best Answer 

 #1
avatar+78754 
+13

We have....using the Law of Sines.....

sinA / a  = sin B / b

sin A / 7  = sin 49 / 9

So.....

sin-1 (7 * sin 49 / 9)  = A =  about 35.94°

And C = 180 - 49 - 35.94  = 95.06°

So ..to find c, we have

c / sin 95.06  = 9 / sin 49

c = 9 sin 95.06 / sin 49  = 11.88

 

Now to see if we have another triangle...... subtract A from 180 

180 - 35.94 = 144.06

Adding this possible angle to B  = 144.06 + 49  >  180

So....only one triangle exists

A = 35.94   a = 7

B = 49        b = 9

C = 95.06  c = 11.88

 

  

CPhill  May 5, 2015
Sort: 

5+0 Answers

 #1
avatar+78754 
+13
Best Answer

We have....using the Law of Sines.....

sinA / a  = sin B / b

sin A / 7  = sin 49 / 9

So.....

sin-1 (7 * sin 49 / 9)  = A =  about 35.94°

And C = 180 - 49 - 35.94  = 95.06°

So ..to find c, we have

c / sin 95.06  = 9 / sin 49

c = 9 sin 95.06 / sin 49  = 11.88

 

Now to see if we have another triangle...... subtract A from 180 

180 - 35.94 = 144.06

Adding this possible angle to B  = 144.06 + 49  >  180

So....only one triangle exists

A = 35.94   a = 7

B = 49        b = 9

C = 95.06  c = 11.88

 

  

CPhill  May 5, 2015
 #2
avatar+1068 
+5

Two sides and an angle are given. Determine whether the given information results in 1 triangle, 2 triangles, or none at all. a=7 b=9 B=49

a = 7                       B = 49o                                                  

b = 9                       A = 35.94o                     

c = 11.88                 C = 95.06o

 

I'm safe

 

civonamzuk  May 5, 2015
 #3
avatar+91051 
+8

Thanks CPhill and Civonamzuk, 

 

I decided to test my skills with GeoGebra and see how many I could construct.

Each one has 9 on the bottom and 7 on the left.

Each triangle has the angle in a different place with respect to the sides.

I think that they are all different.

I get 4 triangles

 

Oh no I am sorry the angle had to be opposite the 9

In that case I get 1  

Sorry   

 

Melody  May 6, 2015
 #4
avatar+1068 
+5

I guess you are right.

civonamzuk  May 6, 2015
 #5
avatar+91051 
0

Thanks Civonamzuk,

Your presentation was brilliant, you just made a little mistake somewhere - it is no big deal :)

Melody  May 6, 2015

5 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details