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Anastasy [175]
2 years ago
10

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

Mathematics
1 answer:
Ierofanga [76]2 years ago
6 0

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=\sqrt{18}

Hypotenuse=3\sqrt{2}

The three trigonometric ratios are

\sin \theta=\dfrac{Perpendicular}{Hypotenuse}

\sin \theta=\dfrac{3}{3\sqrt{2}}

\sin \theta=\dfrac{1}{\sqrt{2}}

Similarly,

\cos \theta=\dfrac{Base}{Hypotenuse}

\cos \theta=\dfrac{3}{3\sqrt{2}}

\cos \theta=\dfrac{1}{\sqrt{2}}

And,

\tan \theta=\dfrac{Perpendicular}{Base}

\tan \theta=\dfrac{3}{3}

\tan \theta=1

Therefore, the hypotenuse is 3\sqrt{2} cm and three trigonometric ratios are \sin \theta=\dfrac{1}{\sqrt{2}}, \cos \theta=\dfrac{1}{\sqrt{2}}, \tan \theta=1.

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