In triangle ABC, angle C is 90 degrees, AB = 39, AC = 15. Find tg A.

In the triangle ABC we find tg a, if it is known:

Angle C = 90 °;
AB = 39;
AC = 15.

Decision:

1) cos a = AC / AB = 15/39 = (3 * 5) / (3 * 13) = (1 * 5) / (1 * 13) = 5/13;

2) Find sin a from the formula sin ^ 2 a + cos ^ 2 a = 1.

sin a = √ (1 – cos ^ 2 a) = √ (1 – (5/13) ^ 2) = √ (1 – 25/169) = √ (169/169 – 25/169) = √ (144 / 169) = 12/13;

3) Find tg A.

tg a = sin a / cos a = 12/13 / (5/13) = 12/13 * 13/5 = 12/5 = 10/5 + 2/5 = 2 + 0.4 = 2.4;

As a result, we got tg a = 2.4.