Question

In ΔXYZ , XY = 8√3 cm, XZ = 16 cm, YZ = 8 cm, then m∡Z = ?​

Answer 1

Answer:

:)

Step-by-step explanation:

Hope it helps

Answer 2

Answer:

The value of angle Z is 60*

Step-by-step explanation:

Given that,

In ΔXYZ,The lengths of sides are XY=8√3 cm, XZ=16 cm,YZ=8 cm and we are required to find the value of angle Z.

According to cosine relation for triangles,the cosine of the required angle is found as follows

$cosZ=\frac{YZ^{2}+XZ^{2}-XY^{2}}{2(YZ)(XZ)}$

Substituting the lengths of given sides in the above relation,we get

$cosZ=\frac{8^{2}+16^{2}-(8\sqrt{3})^{2}}{2(8)(16)} \\=\frac{64+256-192}{256} =\frac{128}{256} =\frac{1}{2} \\= > Z=cos^{-1}(\frac{1}{2})=60^{0}$

Therefore,

The value of angle Z is 60*

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