Find the length of the longest side of the triangle if the perimeter is 23.

12 units

Step-by-step explanation:

We are told that the perimeter of this triangle is 23 units. Since the perimeter of a triangle is the sum of its three sides, we right this sum using for each side the expression that they show in the picture.

Perimeter =

Therefore, the value of the unknown "x" which appears in the expressions for all of the three sides, is 3 units.

Then, the side: 3x-5 = 3(3)-5 = 9-5 = 4 units

the side 2x+1 = 2(3)+1 = 6+1 = 7 units

and the side 4x = 4(3) = 12 units (therefore this is the longest side).

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2