Which Pythagorean?

Geometry Level 1

$\sin\theta =\dfrac 38$

If $\tan^2\theta=\frac { m }{ n },$ where $m$ and $n$ are coprime positive integers, find $mn.$

2 solutions

Kay Xspre
Mar 13, 2016

$\tan^2(x) = \frac{\sin^2(x)}{1-\sin^2(x)} = \frac{\frac{9}{64}}{1-\frac{9}{64}} = \frac{9}{55}\Rightarrow mn = 495$

is this a formula you used? if yes, then what part of the 8 fundamental identities is this?

Louis Jayson Santos - 3 years, 4 months ago

Susanna Kraeski
Mar 29, 2021

If $\sin \theta = \frac{3}{8}$ , then by Pythagorean theorem $\tan \theta = \frac{3}{\sqrt{55}}$ ⇒ $\tan^2 \theta = \frac{9}{55}$ ⇒ $\ mn = 495$