Question

The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible,solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by: a = 20.5, b = 350, B=25a = 140.7*. y = 14.3.c =40.6c=14.3*.y = 140.7.c = 52.4No triangle can be formed from this information:Two triangles may be formed.

Answer 1

The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle possible, or two triangles possible. If only one triangle is possible,

solve the triangle. If either two triangles may be formed or no triangle may be formed, say so. The triangle is defined by: a = 20.5, b = 35.0, B=25

we have

a=20.5

b=35.0

B=25 degrees

step 1

Find the value of angle A

apply the law of sines

a/sinA=b/sinB

20.5/sinA=35.0/sin25

sinA=(20.5*sin25)/35.0

A=14.3 degrees

step 2

Find the value of angle C

REmember that

A+B+C=180

14.3+25+C=180

C=140.7 degrees

step 3

Find the value of c

Applying the law of sines

c/sinC=b/sinB

c/sin140.7=35.0/sin25

c=(35.0/sin25)*sin140.7

c=52.5

therefore

one triangle possible

option

c=14.3*.y = 140.7.c = 52.4