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Select the angle that correctly completes the law of cosines for this triangle.

Check the final answer first, then review the worked steps.

Answer

28°

Step-by-step solution

  1. Identify the Law of Cosines: The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The general form is $c^2 = a^2 + b^2 - 2ab \cos(C)$, where $C$ is the angle opposite side $c$. The problem provides an equation that is a rearrangement of this law: $8^2 + 17^2 - 2(8)(17)\cos(\_) = 15^2$. This equation is set up to find the angle opposite the side with length 15.
  2. Match the equation to the triangle: In the given equation, we have sides of lengths 8 and 17, and the result is $15^2$. This means that the sides $a$ and $b$ in the Law of Cosines formula are 8 and 17 (or vice versa), and the side $c$ is 15. The angle we need to find is the angle $C$ opposite the side with length 15.
  3. Locate the angle opposite the side of length 15: Examine the provided triangle. The side with length 15 is the base. The angle opposite this side is the angle between the sides with lengths 8 and 17. This angle is given as $28^\circ$.
  4. Complete the equation: Substitute the identified angle into the provided equation. The equation is $8^2 + 17^2 - 2(8)(17)\cos(\_) = 15^2$. The angle opposite the side of length 15 is $28^\circ$. Therefore, the equation becomes $8^2 + 17^2 - 2(8)(17)\cos(28^\circ) = 15^2$.