problem 1 if you cut that equilateral triangle in half, the "half" is a 30-60 right triangle. The proportions are 1 (side), 2 (hypotenuse), squareroot of 3 (in this case, the height). So the ratio of the height to a side is (square root of 3)x : 2x
Last edit: 2008-04-19 06:29:22
ieatkids5 United States. April 19 2008 06:31. Posts 4385
altitudes of an equilateral triangle form a 30-60-90 triangle, so the side opposite of the 60 angle (the untouched angle) is equal to (radical 3)/2 of the hypotenuse. therefore, the ratio is (radical 3)/2
when a binomial(an expression with 2 different terms) is squared, you can follow the equation a squared (where a is the first term) + 2ab (where b is the second term) + b squared or a squared - 2ab + b squared, depending on the symbols. since you're subtracting, you follow a squared - 2ab + b squared.
to rationalize #4, multiply the denominator by its conjugate ( root 14 + root 2). you do foil, and the middle term cancels out and you're left with 14 - 2.
but keep in mind, when you multiply it by the conjugate, you multiply both the numerator and the denominator by the conjugate,which is the same thing as multiplying the entire term by 1 - which is why it is the same thing, right?