Question

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

Answer 1

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`.