Mathematics: Triangle XYZ, X equals 27 cm, Y equals 79 cm and angle C equals 142Degrees. Find the length of Z, to the nearest centimeter.

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Triangle XYZ, X equals 27 cm, Y equals 79 cm and

Baby010391

16.03.2022

Given:

In triangle XYZ, x = 27 cm, y = 79 cm and $\angle C=142^\circ$ .

To find:

The length of z.

Solution:

In triangle XYZ, using the Law of cosine, we get

$z^2=x^2+y^2-2xy\cos Z$

Putting the given values in the above formula, we get

$z^2=(27)^2+(79)^2-2(27)(79)\cos (142^\circ)$

z^2=729+6241-4266(-0.788)

z^2=6970+3361.608

z^2=10331.608

Taking square root on both sides.

$z=\pm \sqrt{10331.608}$

$z=\pm 101.6445178$

Approx the above value to the nearest number and side length cannot be negative. So,

$z\approx \pm 102\text{ cm}$

Therefore, the length of z is about 102 cm.

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