The length of BA in the given triangle where angle A is 90 degrees and has an altitude AD would be 31.2. The value is found by using the concept of similarity of triangles.
As we can see in the given figure that triangle BAC is a right angle triangle where AD is an altitude and point D is on the line BC.
We need to find the value of BA.
So , in order to find the value of BA we would use the concept of similarity of triangles.
In triangle BAC and triangle ADC.
angle A = angle D ( 90 degree)
AC = AC ( common side)
angle C = angle C ( common)
So , by ASA similarity we can say that triangle BAC is similar to triangle ADC.
Now , we know that if 2 triangles are similar then their sides are going to be equal in measure :
BA/AD = AC/DC = BC/AC.
x / 12 = 13/5 ( assuming BA as x)
Cross multiplying :
156 = 5x
x = 31.2
So , the value of x or the value of BA is going to be 31.2.
The question probable may be:
Segment AD is an altitude of triangle ABC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
If AD = 12, DC = 5, and AC = 13, find BA. Round to the tenths place if necessary.
33.4
31.2
5.4
4.6