Question

In ∆ XYZ, XY = 6√3 cm, YZ = 12 cm, XZ = 6 cm then find the measure of ∠X and ∠Z.​

Answer 1

Answer:

In a triangle XYZ, angle Y is right angle.

So, Hypotenuse is XZ=17cm

YZ=15cm

Pythagoras theorem says:

XZ^2=XY^2+YZ^2

XY^2=17^2-15^2

XY^2=64

= > XY=8cm

Sin X= Opposite side of angle X / Hypotenuse

=YZ/XZ

Sin X = 15/17

Cos Z =Adjacent side of angle Z / / Hypotenuse

=YZ/XZ

Cos Z = 15/17

Tan X = Opposite side of angle X / Adjacent side of angle X

=YZ/XY

Tan X = 15/8

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tgudivadakumar9

Answer 2

Given: XY = 6√3 cm, YZ = 12 cm, XZ = 6 cm

To find: The measure of ∠X and ∠Z

Solution: We can understand from the lengths of the sides of the triangle XYZ that it is a right-angled triangle where,

YZ² = XZ² + XY²​

⇒ (12)² = 6² + (6√3)²

⇒ 144 = 36 + (36 × 3²)

⇒ 144 = 144

Here, angle X is the right angle.

Hence, ∠X = 90°.

To find the angle Z, we find tanZ.

tanZ = XY/XZ

⇒ tanZ =  6√3/6

⇒ tanZ = √3

⇒ Z = 60°

Answer: ∠X = 90°, ∠Z = 60°