Which of the following triangle lengths form right triangles? Select all that apply.

(7, 11, 13)
(10, 24, 26)
(12, 16, 20)
(12, 35, 37)
(13, 15, 19)

Test each set in Pythagorean theorem, since they are right triangles.

a^2+b^2=c^2

a and b are the legs, or the shorter sides, and c is the hypotenuse, or longest side

(7,11,13)

7^2+11^2=13^2

49+121=169

170=169

False

(10,24,26)

10^2+24^2=26^2

100+576=676

676=676

True

(12,16,20)

12^2+16^2=20^2

144+256=400

400=400

True

(12, 35, 37)

12^2+35^2=37^2

144+1225=1369

1369=1369

True

(13, 15, 19)

13^2+15^2=19^2

169+225=361

394=361

False

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

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