In triangle ABC, the angle is 90 degrees, AB is equal to the root of 13, BC is 3. find tgA.

Find tg a in triangle ABC.
It is known:
The angle is 90 °;
AB = √13;
BC = 3.
Decision.
1) tg a = BC / AC (ratio of the opposite leg to the adjacent leg);
Since the hypotenuse and one leg are known, then the second leg can be found.
Let’s find the second leg of the AC.
2) AB ^ 2 = AC ^ 2 + BC ^ 2;
Hence, AC ^ 2 = AB ^ 2 – BC ^ 2;
AC = √ (AB ^ 2 – BC ^ 2) = √ (√13 ^ 2 – 3 ^ 2) = √ (13 – 9) = √4 = 2;
3) Substitute the known values AC = 2 and BC = 3 into the formula tg a = BC / AC, find tg a.
We get:
tg a = 3/2 = 1.5.
Answer: tg a = 1.5.