Finding the length of c

Question

I am not sure if that is an easy or hard question, can c be calculated in this scenario where a and b are known. Appreciate any help.

Answer 1

The answer is no, $c$ cannot be calculated if $a$ and $b$ are known. Let be be $x$ cm. Extend a right angle from $b$ as far as possible. Complete the right triangle and mark off $a$. Note that $c$ depends on how far you extend the right angle from $b$.

Answer 2

Query ambiguous. Depending on how query (i.e. drawing) interpreted, $c$ is either known or unknown.

Let $\theta$ denote the angle formed by the two line segments whose lengths are labeled $a$ and $c$. Presumed that $\theta$ and these two line segments form an inner right triangle.

Presumed that diagram indicates that $b$ is the leg of an outer right triangle, where $c$ is a portion of the other leg and $a$ is a portion of the hypotenuse.

Then, it is clear that $c$ is known if and only if $\theta$ is known.

The question is whether there is some relationship between $a$ and the hypotenuse. For example, if it is to be presumed that the hypotenuse has length $(2a)$, then $\sin(\theta) = (b/2a)$ which implies that $\theta$ is known, which implies that $c$ is known.

Alternatively, if the hypotenuse of the outer right triangle is unknown, then $\theta$ can not possibly be known, which implies that $c$ can not be known.