Question

show that in a right angled triangle the hypotenuse in the longest side

Answer 1

n a right angled triangle, the angle opposite To the hypotenuse is 90°, while other two angles are Always less than 90°. As you know that the side opposite to the largest angle is always the largest in a triangle.

Answer 2

$\huge\underline\mathfrak{Answer:}$

A right-angled triangle ABC in which $\bf\angle$ABC = 90°. We have to prove that AC is the longest side, i.e.,

(i) AC > AB

(ii) AC > BC

In ∆ ABC, WE HAVE

• $\bf\angle$ABC=90°

But $\bf\angle$ABC+$\bf\angle$BCA+$\bf\angle$CAB=180°.

=> 90°+$\bf\angle$BCA+$\bf\angle$CAB=180°.

=> $\bf\angle$BCA+$\bf\angle$CAB=180°-90°

=>$\bf\angle$BCA+$\bf\angle$CAB=90°.

=>$\bf\angle$BCA $\bf\angle$CAB are acute angles

=> $\bf\angle$BCA <90° and $\bf\angle$CAB<90°.

=> $\bf\angle$BCA<$\bf\angle$ABC and $\bf\angle$ABC>$\bf\angle$CAB

=> AC>AB AND AC>BC.