Answer:
9,765 cm
Step-by-step explanation:
We'll solve out the measurements for triangle ABC then it will be easy to figure out x
For triangle ABC, we have
Angle B = 90 degrees.
Angle A (CAB) = 38 degrees (the angle CAD is 19 and is said to be half of CAB, since the line AD is a bisector).
Angle C = 180 - 90 - 38 = 52 degrees.
To find the measurement of the BC line, which we label a, we know that
[tex]\frac{a}{sin(A)} = \frac{c}{sin(c)}[/tex]
So, we can isolate the a to get:
[tex]a = \frac{c * sin(A)}{sin(c)} = \frac{25 * sin(38)}{sin(52)} = 19.53[/tex]
Now we know the segment BC is 19.53 cm.
And we know that segments CD and DB are equal, since AD is a bisector, cutting the CAB angle in half.
So, CD is half of BC.... so 19.53 / 2 = 9.765 cm
