Question

Triangle U S T is shown. Angle U S T is 100 degrees. The length of U S is 9, the length of S T is 10, and the length of U T is s.
Which equation correctly uses the law of cosines to solve for the length s?

92 = s2 + 102 – 2(s)(10)cos(100°)
9 = s + 10 – 2(s)(10)cos(100°)
102 = s2 + 100 – 2(s)(10)cos(100°)
s2 = 92 + 102 – 2(9)(10)cos(100°)

Answer 1

By solving through law of cosines the length s can be written as $s^{2} =9^{2} +10^{2} -2*9*10cos(100)$.

Given the length of US is 9, the length of ST is 10 and the length of UT is s and the angle UST is 100 degrees.

According to law of cosines a length can be written as $c^{2} =a^{2} +b^{2} -2abcos g$

where c is the side opposite to the given angle and a and b are other sides , g is the angle given.

$s^{2} =9^{2} +10^{2} -2*9*10cos(100)$

where s is the length of the side opposite to the angle given, the length of other sides are 9 and 10 where the angle is 100.

Hence the fourth option is correct which is s^{2} =9^{2} +10^{2} -2*9*10cos(100).

Learn more about trigonometric functions here https://brainly.com/question/24349828

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