Question

in triangle xyz angle x y z is equal to 90 degree angle y z is equal to 60 degree angle y z x is equal to 30 degree and xy is equal to 4 cm then find x z​

Answer 1

The value of XZ is 8 cm

Step-by-step explanation:

Given data

• ΔXYZ is a right angle triangle.

        ∠ XYZ = 90°

        ∠ YZX = 30°

        XY = 4 cm

        XZ = Hypotenuse (because it is opposite to 90°)

• From trigonometry relation

        $\mathbf{\sin \angle YZX =\frac{Perpendicular}{hypotenuse}}$

• On putting respective value in above equation

        $\mathbf{\sin 30 =\frac{XY}{XZ}}$

• On putting the value of XY and sin 30° in above, we get

          $\mathbf{\frac{1}{2} =\frac{4}{XZ}}$

         By cross multiplication

         XZ = 8 cm