ABC is a triangle with a right angle at A. M and N are points on BC such that AM is the altitude, and AN is the angle bisector of ∠BAC. If CN/NB=21, what is CM/MB?

Already answered.

21^2=441

THANKS:D

To find the ratio CM/MB, we can use the angle bisector theorem.

The angle bisector theorem states that in a triangle, if a line divides any of the angles into two equal angles, then it divides the opposite side in the same ratio as the other two sides.

In this case, since AN is the angle bisector of ∠BAC, it divides BC into two segments, CN and NB. We are given that CN/NB = 21.

Since CM is the altitude, it is perpendicular to AB. This means that ∠CMA = 90 degrees.

Now let's proceed with solving the problem:

Since CN/NB = 21, we know that the ratio of the lengths of the segments CN and NB is 21:1.

Let's represent CM as "x" and MB as "y".

Using the angle bisector theorem, we can write:

CN/NB = CM/MB

Substituting the given ratio, we have:

21 = x/y

To find the ratio CM/MB, we just need to solve for x/y.

Cross-multiplying the equation gives us:

21y = x

Rearranging the equation, we find:

x/y = 21

So, the ratio CM/MB is 21:1.

Therefore, CM/MB = 21.