Question

in triangle xyz , angle xyz =90° , angle yxz =60° , angle yzx=30° and xy= 4cm then find xz​

Answer 1

Answer:

sin60 = 1/2 so xy/xz= 4*2= 8

Answer 2

The value of $xz$ is $8\ cm$

Step-by-step explanation:

Given,

$\triangle xyz$ where $\angle xyz=90\ degree\ and\ \angle yxz=60\ degree\ and\ \angle yzx=30\ degree\ and\ xy=4\ cm$

We know,

$cos \theta=\frac{Adjacent}{Hypotenuse}$ and $tan\theta=\frac{Opposite}{Adjacent}$

From figure,

$cos 60=\frac{xy}{xz}$

⇒$xz=\frac{4}{\frac{1}{2} }$

⇒$xz=8\ cm$

Another way,

$tan30=\frac{xy}{yz}$

⇒$yz=\frac{4}{\frac{1}{\sqrt{3}} }$

⇒$yz=4\sqrt{3}$

$\triangle xyz$ is right-angle triangle,

Using Pythagoras Theorem,

$xz=\sqrt{(xy)^{2}+(yz)^{2} }$

⇒$xz=\sqrt{(4)^{2}+(4\sqrt{3})^{2} }$

⇒$xz=\sqrt{16+48}$

⇒$xz=\sqrt{64}$

⇒$xz=8\ cm$

So, The value of $xz$ is $8\ cm$