Respuesta :

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We can solve the length of u using Laws of Cosine since we are given with lengths of two side and one angle.
The solution is shown below:
cos U =( s²+t²-u²)/2st
cos 37°= (9²+15²-u²)/2*9*15
0.79863*270=306-u²
u²=306-215.63
u=9.5 units
Therefore, the length of u is 9.5cm.

The measure of u is about 9.51 cm.

Important information:

  • In triangle STU, s = 9 cm, t = 15 cm
  • The measure of angle U is 37 degrees.
  • We need to find the length of u.

Law of Cosines:

Using the Law of Cosine, we get

[tex]u^2=s^2+t^2-2st\cos U[/tex]

[tex]u^2=(9)^2+(15)^2-2(9)(15)\cos (37)[/tex]

[tex]u^2=81+225-215.63[/tex]

[tex]u^2=90.37[/tex]

Taking square root on both sides, we get

[tex]u=\sqrt{90.37}[/tex]

[tex]u\approx 9.51[/tex]

Therefore, the measure of u is about 9.51 cm.

Find out more about 'Law of Cosines' here:

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