Question

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

Answer 1

Answer:

One

Step-by-step explanation:

Find the value of B

Applying the law of sines

$\frac{a}{sin(A)}$ = $\frac{b}{sin(B)}$

substitute the given values

$\frac{23}{sin(61)}$ = $\frac{24}{sin(B)}$

sin (B) = $\frac{24}{23}$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

$\frac{a}{sin(A)}$ = $\frac{c}{sin(C)}$

substitute the given values

$\frac{23}{sin(61)}$ = $\frac{c}{sin(53.13)}$

c = $\frac{23}{sin(61)}$SIN (53.13)

C=21.04 units

so

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