Question

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

A = 61°, a = 23, b = 24

Answer 1

The answer is 2 triangles

Explanation:

I took the test.

Answer 2

One

Explanation:

Find the value of B

Applying the law of sines

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

substitute the given values

`(23)/(sin(61))` =
`(24)/(sin(B))`

sin (B) =
`(24)/(23)`Sin(61)

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 + 65.87 + C = 180

C = 53.13

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))` =
`(c)/(sin(53.13))`

c =
`(23)/(sin(61))`SIN (53.13)

C=21.04 units

so

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