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Oksanka [162]
3 years ago
11

Right triangle XYZ has right angle Z. If the sin(X)=1213 , what is the cos(X)

Mathematics
1 answer:
AlekseyPX3 years ago
6 0

Given:

Right triangle XYZ has right angle Z.

\sin(x)=\dfrac{12}{13}

To find:

The value of \cos x.

Solution:

We know that,

\sin^2(x)+\cos^2(x)=1

\cos^2(x)=1-\sin^2(x)

\cos(x)=\pm\sqrt{1-\sin^2x}

For a triangle, all trigonometric ratios are positive. So,

\cos(x)=\sqrt{1-\sin^2x}

It is given that \sin(x)=\dfrac{12}{13}. After substituting this value in the above equation, we get

\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}

\cos(x)=\sqrt{1-\dfrac{144}{169}}

\cos(x)=\sqrt{\dfrac{169-144}{169}}

\cos(x)=\sqrt{\dfrac{25}{169}}

On further simplification, we get

\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}

\cos(x)=\dfrac{5}{13}

Therefore, the required value is \cos(x)=\dfrac{5}{13}.

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