D(5,7) e (4,3) and f(8,2) from the vertices of a triangle what is m def

m∠DEF = 90°

Step-by-step explanation:

As we know to determine the angle between two lines with the given equations or vertices we use the formula

Now we have been given the vertices of a triangle as D(5, 7) E(4, 3) F(8, 2)

To measure m∠ DEF will use the formula

Since slope of DE

Slope of EF

Now m∠DEF =

Therefore

Answer is ∠DEF = 90°

m<DEF = 90°

Step-by-step explanation:

It is given that, D, E and F are the vertices of a triangle.

D(5,7) E (4,3) and f(8,2)

To find side DE

D(5,7) E (4,3)

DE = √[(5-4)² + (7 - 3)²] = √17

To find side  EF

E (4,3) ,F(8,2)

EF = √[(8-4)² + (2 - 3)²] = √17

To find side  DF

D(5,7)  ,F(8,2)

EF = √[(8-5)² + (2 - 7)²] = √34 = √2√17

To find the ratio of sides

The sides are in the ratio

DE : EF : DF = √17 : √17 : √2√17 = 1 : 1 : √2

To find the angle DEF

The sides are in the ratio 1 : 1 : √2

Therefore triangle DEF is a right angled triangle.

DE = EF

<DEF = 90°

7. 153.86 ft

8. 12.56 ft

9. 78.5 m

10. 379.94 in

11. 132.665 m

12. 12.56 yd

13. 226.865 ft

14. 113.04 ft

15. 63.585 ft

16. 254.34 m

17. 50.24 cm

step-by-step explanation:

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.