Question

The triangle ABC have two equal sides where AB = 10 cm, And BC = 10 cm, what Is the length of CA?

Answer 1

There is no single answer for this question.

The side `CA` can have any length between 0 and 20 cm. To calculate the exact length more data is needed. The task is in Trigonometry, so probably the angle is missing.

For example:

Suppose you have an angle B

If the angle was 60 degrees, all sides would be equal, so `|CA|=10`
However if the angle was 90 degrees, the `CA` would be a hypothenuse and would be `10sqrt2` cm long.

Generally if the angle was `alpha` you could calculate a general formula using law of cosines.

`|CA|^2=|CB|^2+|AB|^2-2|CB||AB|cos alpha`, so

`|CA|=sqrt(|CB|^2+|AB|^2-2|CB||AB|cos alpha)`