Question

In triangle XYX,right angles is at Y ,YZ= x and XZ = 2x .Then determine $\angle{YXZ}$ and $\angle{YZX}$

Answer 1

Answer:

Step-by-step explanation:

Given ,

In Triangle XYZ , $\angle{Y}$ = 90°

YZ = x units , XZ = 2x units

In Triangle XYZ , Angle Y = 90°

Sin X = YZ/XZ

= x/22x

= 1/2

We know that ,sin 30° = 1/2

So , Sin X = sin 30°

=> x = 30°

In Triangles XYZ,

Angle X + Angle Y +Angle Z = 180°.(Angle sum property )

30° +90° + Angle Z = 180°

120° + Angle Z = 180°

Angle Z = 180°-120°

Angle Z = 60°

So ,

$\angle{YXZ}$ = Angle X = 30° and

$\angle{XYZ}$ = Angle Z = 60°

Answer 2

Answer:

$\huge\mathfrak{Answer:60°}$

Given that :-

• In triangle XYX,right angles is at Y ,YZ= x and XZ = 2x .

To find :-

• Then determine angle
• YXZ and YZX.

Solution:-

Sin x = opposite side of x/hypotenuse

⇒ x/2x = 1/2

Sin x = 1/2 = Sin 30°

⇒ x = 30° or ∠ YXZ = 30°

Cos Z = Adjacent side of z/hypotenuse

⇒ x/2x = 1/2 

⇒ Cos Z = 1/2 = Cos 60°

Answer :- Z = 60° = ∠ YZX = 60°