Question

I need to work out x

Answer 1

9,765 cm

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

`(a)/(sin(A)) = (c)/(sin(c))`

So, we can isolate the a to get:

`a = (c * sin(A))/(sin(c)) = (25 * sin(38))/(sin(52)) = 19.53`

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