Question

2. How many triangle(s) can you make for each problem from the given information? Graph and show your work. Keep your answers in one decimal place, calculator ok. a) A-65°, a = 18m b = 22. b) A= 58°, a = 20, b = 22. dimit ftor decimal calculator

Answer 1

Solution

1)

find sinB and if

sinB<1 then two triangles are possible

sinB=1 then one triangle is possible

sinB>1 then no triangles are possible

here use law of sine

sinA/a=sinB/b

sinB=b×sinA/a=22×sin65°/18=1.11

sinB>1

therefore, no triangles are possible as maximum value of sin is 1

2)use law of sine to find sinB

SinB=b×sinA/a=22×sin58°/20=0.9328

so, sinB<1 hence, two triangles are possible

B=arcsin(0.9328)=68.9°

and also, sin is positive in second quadrant so,

B=180°-68.9°=111.1°

now, finding other values with B=68.9°

by angle sum property

C=180°-A-B=180°-58°-68.9°=53.1°

by law of sine

sinC/c=sinA/a

c=a×sinC/sinA=20×sin53.1°/sin58°=19.1

now solving other values with B=111.1°

by angle sum property

C=180°-58°-111.1°=10.9°

use law of sine

c=a×sinC/sinA=20×sin10.9°/sin58°=4.5

therefore, other values of first triangle are B=68.9°, c=19.1, C=53.1°

and other values of second triangle are B=111.1°, c=4.5 and C=10.9°