Can a triangle be both acute and isosceles? Justify your reasoning.

No. There can be an obtuse angle or a right-angle in an isosceles triangle.

Step-by-step explanation:

Explanation:

No. You can three types of isosceles triangles:

acute-angled isosceles triangle

All the angles are acute and the base angles are equal.

eg:  

75 ° , 75 ° , 30 °

 or  

50 ° , 50 ° , 80 °

right-angled isosceles triangle

One angle is  90 °  and the other two are both  45 °

45 ° , 45 ° , 90 °

   ←    

(like one of the usual set squares)

obtuse-angles isosceles triangle

One angle is obtuse and the base angles are equal.

eg:  

30 ° , 30 ° , 120 °

 or  

25 ° , 25 ° , 130 °

Ofcourse there can only be one  90 °

or

one obtuse angle in a triangle. The other two angles MUST be acute, else the sum would be more than  180 °

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

i think the length is 12 and the width is 17