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

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

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Answer 1 · 2015-05-21T08:30:09

There is no single answer for this question.

The side $C A$ $CA$ 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 $| C A | = 10$ $|CA|=10$
However if the angle was 90 degrees, the $C A$ $CA$ would be a hypothenuse and would be $10 \sqrt{2}$ $10sqrt2$ cm long.

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

${| C A |}^{2} = {| C B |}^{2} + {| A B |}^{2} - 2 | C B | | A B | cos α$ $|CA|^2=|CB|^2+|AB|^2-2|CB||AB|cos alpha$ , so

$| C A | = \sqrt{{| C B |}^{2} + {| A B |}^{2} - 2 | C B | | A B | cos α}$ $|CA|=sqrt(|CB|^2+|AB|^2-2|CB||AB|cos alpha)$

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

1 Answer

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