Join the IDNLearn.com community and get your questions answered by experts. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.
Sagot :
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.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.
