MathDB

a,b,c form right angle triangle as well as 1/a,1/b,1/c

Source:

May 20, 2012

trigonometrygeometry

Problem Statement

Let

a,b

and

c

be the sides of a right angled triangle. Let

\theta

be the smallest angle of this triangle. If

\frac{1}{a}, \frac{1}{b}

and

\frac{1}{c}

are also the sides of a right angled triangle then show that

\sin\theta=\frac{\sqrt{5}-1}{2}