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

January 13, 2021 | education

| 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.

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