Question

in right angle triangle ∆XYZ angle XYZ 90° YT 8s perpendicular to XZ then prove that XY²= XT*YT​

Answer 1

$\huge\red{A}\pink{N}\orange{S} \green{W}\blue{E}\gray{R} =$

Let XY Z is a right angle triangle

YZ = X, XZ = 2x, 2Y = 90°

By using Pythagoras theorem

XZ² = XY2+ YZ²

XY 2 = XZ² - YZ²

= (2x)²(x)² = 4x² - x² = 3x²

.. XY = √√√3x² = √3x

From AXY Z

$\huge\red{tan \: x = \frac{yz}{xy} = \frac{x}{ \sqrt{3 x } } = \frac{1}{ \sqrt{3 } } = \tan \: 30°}$

⇒ <Y XZ = 30°

$\huge\red{tan \: z = \frac{XY}{YZ} = \frac{ \sqrt{3x} }{x} = \sqrt{3} = tan60° }$

→ Y ZX = 60°

$\huge.. <Y XZ = 30° and \: ZY \: XZ = 60°$