The following calculator can figure out the length of all sides of a right angle triangle using only the area and a angle. How is it doing that..?
http://www.triangle-calculator.com/?what=rt&a=T%3D17.5+A%3D35.538&submit=Solve
[Math] Finding all sides of a right triangle from area and a angle
geometrytrianglestrigonometry
Related Solutions
Hint: $\bigtriangleup DCE \sim \bigtriangleup ABE$ as $BC$ is crossing parallel lines.
Not enough informations. Assume that $\widehat{ABC}=\widehat{A'B'C'}$ and $AB\cdot BC = A'B'\cdot B'C'$.
Then the triangles $ABC, A'B'C'$ have the same area and share an angle, but they are not necessarily congruent:
Best Answer
Lets say you are given one of the angles and lets call this angle $\alpha$.
Lets call the side opposite $\alpha$, $a$ and the side adjacent to $\alpha$, $b$.
Finally lets call the area of this triangle $A$.
We can then say that:$$\tan(\alpha)=\frac{a}{b}\tag{1}$$
and:$$A=\frac{1}{2}ab\tag{2}$$ From (2) we get:$$b=\frac{2A}{a}\tag{3}$$and if we substitute this into (1) we get:$$\tan(\alpha)=\frac{a}{\frac{2A}{b}}=\frac{a^2}{2A}$$$$\therefore a^2=2A\tan(\alpha)\tag{4}$$You can therefore calculate $a$ from (4) and then get $b$ from (3) and use pytharous to get the remaining side.