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

Question

asked Feb 15, 2017 202k views

2 Answers

Chia · Answer 1 · 2017-02-20T23:05:01+0000

Answer:

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