Math CentralQuandaries & Queries


Question from Megan, a student:

Find the perimeter of an isoselese triangle with a verticle angle ofAn isoselese triangle 100 degrees and a base of 25 cm.

I think I could answer this if I knew what a verticle angle was.

Hi Megan. I never heard of "verticle angle" before either.

However, this is an isosceles triangle, so two angles must match. Since all triangles have the property that the sum of the measures of their angles is 180, then a 100 degree angle cannot be one of the paired angles, because that puts the total over 200 degrees.

That means that the angles of the triangle are 100, 40 and 40. I subtracted the 100 from the total of 180 leaving 80 degrees split equally into two parts to satisfy the isosceles requirement.

If you consider that "vertical angle" perhaps refers to placing the triangle such that the unique angle is at the top and opens downward (one of two vertical directions), then the unique side would be oriented left-right along the bottom, forming a base. This base, the side opposite the unique 100 degree angle is the one which is 25 cm long.

Now you should have a clear enough idea of the triangle to finish the problem using trig.

Stephen La Rocque.

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