Problem
Let $a,b$ and $c$ be the sides of a right angled triangle. Let $ \displaystyle{\theta } $ be the smallest angle of this triangle. If $ \displaystyle{ \frac{1}{a}, \frac{1}{b} } $ and $ \displaystyle{ \frac{1}{c} }$ are also the sides of a right angled triangle then show that $ \displaystyle{ \sin\theta=\frac{\sqrt{5}-1}{2}}$
Topic
Biquadratic Equations
Main Idea
It is usually hard to solve biquadratic equations. However, sometimes, combining tools from geometry and strategies like completing the square it is possible to do so.
Source
I.S.I. B.Stat. Entrance 2005, Subject Problem 1
Suggested Book
Challenges and Thrills in Pre College Mathematics
Excursion Of Mathematics
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