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Which equation can be used to find the unknown side length?

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Which equation can be used to find the unknown side length?
k² = 7² + 23² – 2 · 7 · 23 · cos 15°
7² = k² + 23² – 2 · k · 23 · cos 132°
k/sin 15° = 7/sin 33°
23² = 7² + k²




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    1 Answer

    1. Quizzma Team

      To find the unknown side length in a triangle using the given options, we can determine which equation relates the sides and angles appropriately.

      The best equation from the list is:

      k² = 7² + 23² – 2 · 7 · 23 · cos 15°

      This equation is derived from the Law of Cosines, which states:

      c² = a² + b² – 2ab · cos(C)

      where c is the side opposite the angle C, and a and b are the other two sides.

      In this equation, you can solve for k (the unknown side length) when you know the lengths of the other two sides (7 and 23) and the included angle (15°).

      Make sure to use a calculator to evaluate cos(15°) and substitute the values to find the length of k. If you’d like more detailed assistance, feel free to check our extended services page for further help!

    3. Quizzma Team

      The equation that can be used to find the unknown side length ‘k’ is:

      k/sin 15° = 7/sin 33°

      This equation is derived from the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle. Here, you can find ‘k’ by rearranging the equation to solve for it.

      Let me know if you have more questions!

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