If the polygon is an equilateral triangle where each side is 24 inches long what is the apothem?
To find the apothem of an equilateral triangle, you can use the formula:
Apothem = (Side Length) / (2 * tan(π / number of sides))
In this case, the equilateral triangle has a side length of 24 inches, and since it is a triangle, the number of sides is 3.
Plugging in these values into the formula, we get:
Apothem = (24) / (2 * tan(π / 3))
To evaluate the tangent function, we need to convert π / 3 to radians:
π / 3 ≈ 1.0472 radians
Now we can substitute the value into the formula:
Apothem = (24) / (2 * tan(1.0472))
Using a scientific calculator, we can compute the tangent of 1.0472:
tan(1.0472) ≈ 1.732
Finally, we substitute this value back into the formula to find the apothem:
Apothem = (24) / (2 * 1.732)
Apothem ≈ 6.928 inches
Therefore, the apothem of the equilateral triangle with a side length of 24 inches is approximately 6.928 inches.