Mike Sweat
12-15-2003, 9:08 PM
With an isosceles triangle. Base is 24", base angles are both 72°, top angle is 36°. What is the length of the sides, and the formula used to calculate this?
Chris Padilla
12-15-2003, 9:47 PM
Turn it into a right triangle with angles of 72°, 90° and half of 36° or 18°. The base is now 12" with this method.
You'll need to use those sin, cos, tan buttons on your calculator.
For example, sin x = opposite/hypontenuse
cos x = adjacent/hypontenuse
tan x = opposite/adjacent
The hypontenuse is is the longest side of the triangle and opposite the 90° angle. In order to figure out what is adjacent or opposite, you need to first start at one of the angles except the 90° one. These are your length measurements. The x will be your angle measurements.
In your case, cos 72° = 12/h or h = 12/cos 72° which is 38.832--this is the length you are looking for.
Now that you have 2 sides, you can use the Pythagorean Theory of:
hypontenuse^2 = (1 side of right triangle)^2 + (the other side of the right triangle)^2.
In your case, 38.832^2 = 12^2 + b^2, b = height of your isosoceles triangle or 36.932.
Or, you could use the trig functions again:
cos 18° = (height of isosoceles triangle)/(38.832), height = 36.932
or
sin 72° = (height of isosoceles triangle)/(38.832), height = 36.932
For more fun and example,
tan 18° = (1 side of the triangle you already know but just checking your work)/(the height of the triangle, 36.932).
What should you get for that last one? It should be 12...half of the base.
Chris
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