Question

In right angled ∆XYZ XY = 5, ∠Y = 90° , YZ= 12 then find sin x , cos X, tan X and also find sin z, cos Z, tan Z​

Answer 1

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Answer 2

Trigonometric ratios

Given:

A triangle XYZ with 90° at Y.

$XY=5 \\YZ=12$

To find:

$sinX, cos X, tanX, sinZ, cosZ, tanZ$

Explanation:

In ΔXYZ, we can apply Pythagoras theorem,

According to Pythagoras theorem,

$p^{2}+ b^{2}= h^{2}$,

So, $XY^{2}+ YZ^{2}= XZ^{2}$

$5^{2}+ 12^{2} =XZ^{2} \\25+144=XZ^{2} \\169=XZ^{2}\\13=XZ$

We know that ,

$sinx= \frac{p}{h}\\\\cosx=\frac{b}{h}\\\\tanx=\frac{p}{b}$

where p is perpendicular, b is base, h is hypotenuse of any right angled triangle.

So,

$sinX=\frac{12}{13}\\\\cos X=\frac{5}{13}\\\\tanX=\frac{12}{5}\\\\sinZ=\frac{5}{13}\\\\cos Z=\frac{12}{13}\\\\tanZ=\frac{5}{12}$

Hence required angles are as shown in figure attached.