Respuesta :
Given:
In triangle XYZ, x = 27 cm, y = 79 cm and [tex]\angle C=142^\circ[/tex].
To find:
The length of z.
Solution:
In triangle XYZ, using the Law of cosine, we get
[tex]z^2=x^2+y^2-2xy\cos Z[/tex]
Putting the given values in the above formula, we get
[tex]z^2=(27)^2+(79)^2-2(27)(79)\cos (142^\circ)[/tex]
[tex]z^2=729+6241-4266(-0.788)[/tex]
[tex]z^2=6970+3361.608[/tex]
[tex]z^2=10331.608[/tex]
Taking square root on both sides.
[tex]z=\pm \sqrt{10331.608}[/tex]
[tex]z=\pm 101.6445178[/tex]
Approx the above value to the nearest number and side length cannot be negative. So,
[tex]z\approx \pm 102\text{ cm}[/tex]
Therefore, the length of z is about 102 cm.
