Question

The base of the isosceles triangle is five times the height Find the exact value of cot ø

Answer 1

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

$AB=BC$

$m\angle BAC=m\angle ACB=\phi^o$

In the right triangle ABD

$cot(\phi)=\frac{AD}{BD}$ ---> adjacent side angle ∅ divided by the opposite side angle ∅

we have

The base of the isosceles triangle is five times the height

so

$b=5h$

$AD=\frac{b}{2}=\frac{5h}{2}\ units$

$BD=h\ units$

substitute

$cot(\phi)=\frac{(5h/2)}{h}=2.5$