Question

suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120°. which equation should you solve to find the length of the third side of the triangle?

a. \\(c^2 = 42^2 + 35^2 - 2(42)(35)\sin 120^\circ\\)
b. \\(\frac{\sin 42}{120} = \frac{\sin 35}{b}\\)
c. \\(c = 42 + 35 - 2(42)(35)\cos 120^\circ\\)
d. \\(c^2 = 42^2 + 35^2 - 2(42)(35)\cos 120^\circ\\)

Explanation:

Identify the given values and target unknown

$$
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$$

Apply the Law of Cosines

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

Substitute the given values into the formula

$$ c^2 = 42^2 + 35^2 - 2(42)(35)\cos(120^\circ) $$

Answer:

• A. \(c^2 = 42^2 + 35^2 - 2(42)(35)\sin120^\circ\)
• B. \(\frac{\sin42}{120} = \frac{\sin35}{b}\)
• C. \(c = 42 + 35 - 2(42)(35)\cos120^\circ\)
• D. \(c^2 = 42^2 + 35^2 - 2(42)(35)\cos120^\circ\) (Correct answer)