Given b=2,\ a=3, and B=40 (degrees), determine whether this information

pamangking8

pamangking8

Answered question

2021-11-25

Given b=2, a=3, and B=40 (degrees), determine whether this information results in one triangle, two triangles, or no triangle at all. Any resulting triangles should be resolved.

Answer & Explanation

oces3y

oces3y

Beginner2021-11-26Added 21 answers

Step 1
Given thet, the values are b=2, a=3 and B=40
Recall that, the sine formula is asinA=bsinB=csinc
sinAa=sinBb
sinA=a(sinBb)
A=sin1(a×sinBb)
Step 2
Substitute a=3, b=2 and B=40 in A=sin1(a×sinBb)
A=sin1(3×sin(40)2)
=sin1(0.9642)
=1.3023×180π
=74.6162
A=74.6
or
A=18074.6
A=105.4
(105.4+40<180)
Step 3
Let A=74.6 then the angle of C is,
C=18074.640
Use the sine formula to find the value of c.
sinBb=sinCc
c=bsinCsinA
c=2sin65.4sin40
c=2.83
Thus, the possible values of the triangle is
a=3, b=2, c=2.83 and A=74.6, B=40, C=65.4
Step 4
Let A=105.4 then the angle of C is,
C=180105.440
=34.6
Use the sine formula to find the value of c.
sinBb=sinCc

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