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In a right angled triangke abc the perpendicular and the base measure 3 cm find hypotenus and three trignometrice ratios

User Abkothman
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1 Answer

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Given:

In a right angled triangle ABC the perpendicular and the base measure 3 cm.

To find:

The hypotenuse and three trigonometric ratios.

Solution:

Pythagoras theorem:


Hypotenuse^2=Perpendicular^2+Base^2

Use Pythagoras theorem in triangle ABC.


Hypotenuse^2=(3)^2+(3)^2


Hypotenuse^2=9+9


Hypotenuse=√(18)


Hypotenuse=3√(2)

The three trigonometric ratios are


\sin \theta=(Perpendicular)/(Hypotenuse)


\sin \theta=(3)/(3√(2))


\sin \theta=(1)/(√(2))

Similarly,


\cos \theta=(Base)/(Hypotenuse)


\cos \theta=(3)/(3√(2))


\cos \theta=(1)/(√(2))

And,


\tan \theta=(Perpendicular)/(Base)


\tan \theta=(3)/(3)


\tan \theta=1

Therefore, the hypotenuse is
3√(2) cm and three trigonometric ratios are
\sin \theta=(1)/(√(2)), \cos \theta=(1)/(√(2)), \tan \theta=1.

User AhmedMaher
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