Answer:
The exact value of cot(∅) is 2.5
Step-by-step explanation:
The picture of the question in the attached figure
we know that
An isosceles triangle has two equal sides and two equal interior angles
In his problem
[tex]AB=BC[/tex]
[tex]m\angle BAC=m\angle ACB=\phi^o[/tex]
In the right triangle ABD
[tex]cot(\phi)=\frac{AD}{BD}[/tex] ---> adjacent side angle ∅ divided by the opposite side angle ∅
we have
The base of the isosceles triangle is five times the height
so
[tex]b=5h[/tex]
[tex]AD=\frac{b}{2}=\frac{5h}{2}\ units[/tex]
[tex]BD=h\ units[/tex]
substitute
[tex]cot(\phi)=\frac{(5h/2)}{h}=2.5[/tex]
