Question

Which equation correctly uses the law of cosines to solve for the length s?

Answer 1

Answer: Choice D

s^2 = 9^2 + 10^2 - 2(9)(10)cos(100)

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Step-by-step explanation:

Consider the pythaorean theorem

a^2 + b^2 = c^2

which is the same as saying

c^2 = a^2 + b^2

If we tack on "-2ab*cos(C)", then we end up with

c^2 = a^2 + b^2 - 2ab*cos(C)

which is one form of the law of cosines. The side c is opposite angle C, and the two are on opposite sides of the equation. The 'a's and 'b's are on the right side with the angle C.

Note if C = 90 degrees, then cos(C) = cos(90) = 0 which means the whole "-2ab*cos(C)" term goes to 0 and we'd be left with the pythagorean theorem again.

In this case, we replace c with s, replace 'a' with 9, replace b with 10, and C with 100.

Answer 2

Option (4)

Step-by-step explanation:

Cosine rule states,

(UT)² = (SU)² + (ST)² - 2(SU)(ST)cos(∠UST)

Here, UT is the opposite side of angle UST and two sides SU and ST are the adjacent sides.

∠UST is the included angle between SU and ST.

By this formula,

s² = 9² + 10² - 2(9)(10)cos(100°)

Therefore, Option (4) will be the answer.