Question

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

A= 61º, a = 23, b = 24
Zero
Two
One

Answer 1

Answer: These measurements determine two triangles.

Explanation:

Given: A=61º, a=23, b=24

sinA/a=sinB/b

sin61º/23=sinB/24

24sin61º=23sinB

(/23)24sin61º=23sinB(/23)

sin^-1(24sin61º/23)=sin^-1(sinB)

B=65.8737º

***

61º+65.8737º+C=180

C=53.1263º

***

sinA/a=sinC/c

sin61º/23=sin53.1263º/c

csin61º=23sin53.1263º

(/sin61º)csin61º=23sin53.1263º(/sin61º)

c=23sin53.1263º/sin61º

c=21.03667

***

A=61º

B=65.8737º

C=53.1263º

a=23

b=24

c=21.03667

Answer 2

zero

Explanation:

The given measurements are:

A= 61º, a = 23, b = 24

In a triangle, the sum of the angles therein is 180°. A triangle is a figure with three sides.

With internal angles summing up to 180°

To know if the given angles are of a triangle, the must add up to 180°;

So;

Summation = 61 + 23 + 24 = 108°

This is not a triangle.

Therefore, from the summation of the angles given, we can see that they do not add up to the sum of angles within a triangle.