Question

Segment AD is an altitude of triangle ABC. If AD=15, DC=8, and AC=17, find BA.

a) 3
b) 4
c) 5
d) 6
e) 7

Answer 1

To find the length of BA, we can use the similarity of triangles ABC and ADB. Using the Pythagorean theorem, we can solve for the length of AB, which is 12.

Step-by-step explanation:

To find the length of BA, we can use the similarity of triangles ABC and ADB. Since segment AD is an altitude of triangle ABC, it is perpendicular to BC. This means that triangle ADB is a right-angled triangle.

We can use the Pythagorean theorem to find the length of BD, which is equal to 17 - 8 = 9. Using AD = 15 and BD = 9, we can solve for the length of AB:

AB2 = AD2 - BD2
AB2 = 152 - 92
AB2 = 225 - 81
AB2 = 144
AB = sqrt(144) = 12

Therefore, the length of BA is 12.