Knock out the false cosine claims

Exercise and reference answers

Questions

1. Question

   Three of these statements about the Law of Cosines are false.

   Choices

   1. Item

      It handles SAS and SSS triangles

      Correct

      Yes

   2. Explanation

      It was built for oblique triangles, where no angle is 90 degrees.

      Item

      It works only in right triangles

   3. Explanation

      The included angle enters through its cosine, never its sine.

      Item

      It uses the sine of the included angle

   4. Explanation

      The SSS case starts from three sides with no angle known at all.

      Item

      It needs all three angles first

2. Question

   Three of these claims about Heron's formula are false.

   Choices

   1. Item

      It needs the three side lengths

      Correct

      Yes

   2. Explanation

      Heron's formula exists precisely so the height is never needed.

      Item

      It needs the height of the triangle

   3. Explanation

      The letter s is half the perimeter, the semi-perimeter.

      Item

      The letter s means the full perimeter

   4. Explanation

      No angle appears anywhere in the formula.

      Item

      It needs one angle as well

Instructions

Tap away every claim that is false and leave the one true statement standing.

Explanation