Question

Find values for b such that the triangle has (a) one solution, (b) two solutions, and (c) no solution.

A = 36^o , a = 5

Answer 1

Step 1:

(a)

The triangle side is and angle is

The laws of sines :

 

The angle is acute angle.

Recall the relation from the ambiguous case: .

If triangle has one solution and  is an acute angle , then and

and

Substitute , in .

If triangle has one solution, then values of  are  and .

Solution:

(a)

and .

 

Answer 2

Step 1:

(b)

If triangle has two solutions and is an acute angle , then .

Substitute the corresponding value in above formula

Divide each side by

Finally conclude that  .

Step 2:

(c)

If triangle has no solution and is an acute angle, then

Divide each side by

Substitute and in above expression.

.

Solution:

(b)

(c)

.