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FromTheMoon [43]
3 years ago
12

D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m∠DEF?

Mathematics
2 answers:
Roman55 [17]3 years ago
5 0

Answer:

m∠DEF is 90°

Step-by-step explanation:

It is given that  D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. Thus, using the distance formula, we have

DE=\sqrt{(3-7)^2+(4-5)^2}

⇒DE=\sqrt{16+1}

⇒DE=\sqrt{17}

and EF=\sqrt{(2-3)^2+(8-4)^2}

⇒EF=\sqrt{1+16}

⇒EF=\sqrt{17}

Also,  DF=\sqrt{(2-7)^2+(8-6)^2}

⇒DF=\sqrt{25+9}

⇒DF=\sqrt{34}

Now, (DF)^2=(DE)^2+(EF)^2

⇒(\sqrt{34})^2=(\sqrt{17})^2+(\sqrt{17})^2

⇒34=34

Thus, Pythagoras theorem holds.

Hence, m∠DEF is 90°⇒ΔDEF is right angled triangle which is right angled at E.

lakkis [162]3 years ago
3 0
DE^2 = 1 + 16 = 17. 
<span>EF^2 = 16 + 1 = 17. </span>
<span>DF^2 = 9 + 25 = 34. </span>
<span>Since (DE)^2 + (EF)^2 = (DF)^2, 
</span><span> angle E is 90 degrees.
</span><span> DF must be the hypotenuse 
</span>see attachment below

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