Math CentralQuandaries & Queries


Subject: isosceles triangle height
Name: Katrina
Who are you: Other

Is there any way to calculate the height or the length of the equal sides of an isosceles triangle given only the base length and the angles?

Hi Katrina,

Call the triangle ABC and let M be the midpoint of the base BC. Draw a line from A to M. Let h be the length of AM (the height of triangle ABC) and x be the length of MB, half the length of the base. Also let t be the measure of the angle BCA.

Triangle AMC is a right triangle and hence

tan t = h/x and cos t = x/s

Since you know x and t you can find h and s.


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