+0

# 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

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2390
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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

May 5, 2015

#1
+94526
+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

May 5, 2015

#1
+94526
+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
#2
+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

May 5, 2015
#3
+95177
+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

May 6, 2015
#4
+1068
+5

I guess you are right.

May 6, 2015
#5
+95177
0

Thanks Civonamzuk,

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

May 6, 2015