Want this question answered?
10
An SSA triangle is ambiguous.Suppose the triangle is ABC and, with conventional labelling, you know a, b and angle A.Then by the cosine rule, a2 = b2 + c2 - 2bc*Cos(A)This equation will give rise to a quadratic equation in cwhich has 2 solutions. The perimeter is then a + b + c1 or a + b + c2
Any fraction with zero for the denominator. This is because zero cannot be multiplied by any number to be anything but zero - you cannot divide by zero. This is why it is called "undefined."The only exception to this rule is 0/0, which is called indeterminate, because technically any number can satisfy this expression. example:a/b=cwhich means that:a=b*cif b=0, and a is anything other than zero, then no matter what c is, b*c cannot equal a5=0*c cannot be true no matter what.but, if a is zero and b is zero, then c can be anything, and it still works, which is why 0/0 is indeterminate instead of undefined.
Suppose you have a quadratic expression of the form ax^2 + px + q, where a, p and q are constants. Also, a is non-zero because otherwise you do not have a quadratic!The first step is to divide through by a to give x^2 + (p/a)*x + (q/a)To avoid too many fractions, lets us write b = p/a and c = q/a so that the expression becomesx^2 + bx + c (you will often get it given in this form ie with the coefficient of x^2 being 1).To complete the square you need the square of half the coefficient of x.The coefficient of x is b, so half the coefficient of x is b/2 and sothe square of half the coefficient of x is (b^2)/4.x^2 + bx + c => x^2 + bx = - cNow add (b^2)/4 to both sides to give x^2 + bx (b^2)/4= (b^2)/4 - cwhich simplifies to (x + b/2)^2 = 1/4*(b^2 - 4ac)and the square is completed on the left hand side.