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

May 21, 2015

There is no single answer for this question.

The side $C A$ 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 $| C A | = 10$
However if the angle was 90 degrees, the $C A$ would be a hypothenuse and would be $10 \sqrt{2}$ cm long.

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

$| C A {|}^{2} = | C B {|}^{2} + | A B {|}^{2} - 2 | C B | | A B | \cos \alpha$, so

$| C A | = \sqrt{| C B {|}^{2} + | A B {|}^{2} - 2 | C B | | A B | \cos \alpha}$