Determine the number of possible solutions for a triangle with b=37 degrees, a=32, b=27

Two possible solutions

Step-by-step explanation:

we know that

Applying the law of sines

we have

step 1

Find the measure of angle A

substitute the values

The measure of angle A could have two measures

the first measure------->

the second measure ----->

step 2

Find the first measure of angle C

Remember that the sum of the internal angles of a triangle must be equal to  

substitute the values

step 3

Find the first length of side c

substitute the values

therefore

the measures for the first solution of the triangle are

,

,

,

step 4    

Find the second measure of angle C with the second measure of angle A

Remember that the sum of the internal angles of a triangle must be equal to  

substitute the values

step 5

Find the second length of side c

substitute the values

therefore

the measures for the second solution of the triangle are

,

,

,

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

step-by-step explanation:

this is not possible to solve with the info given.   you need at least an one angle somewhere.