A math question

[Mike Sweat]

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]

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

[Mike Sweat]

Thanks Chris!