Question

State whether the given measurements determine zero, one, or two triangles.

A = 61°, a = 23, b = 24
Select one:
a. Zero
b. Two
c. One

Answer 1

c. one is the wrong answer

Explanation:

i just took the test

Answer 2

c. One

Explanation:

step 1

Find the value of B

Applying the law of sines

`(a)/(Sin(A))=(b)/(Sin(B))`

substitute the given values

`(23)/(Sin(61^o))=(24)/(Sin(B))`

`Sin(B)=(24)/(23)Sin(61^o)`

`B=Sin^(-1)((24)/(23)Sin(61^o))=65.87^o`

step 2

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

`61^o+65.87^o+C=180^o`

`C=53.13^o`

step 3

Find the value of c

Applying the law of sines

`(a)/(Sin(A))=(c)/(Sin(C))`

substitute the given values

`(23)/(Sin(61^o))=(c)/(Sin(53.13))`

`c=(23)/(Sin(61^o))Sin(53.13)`

`c=21.04\ units`

so

there can only be one value for each measurement, therefore there can only be one triangle