Hello, Tweety

In a triangle, the largest side has length 2 cm and one of the other sides has length √2 cm.

Given that the area of the triangle is 1 cm², show that the triangle is right-angled and isosceles. Code:

*
* *
_ * *
√2 * *
* *
* θ *
* * * * * * *
2

Formula: .$\displaystyle A \;=\;\frac{1}{2}\,bc\sin A$

The area is one-half the product of two sides and the sine of the included angle.

We have: .$\displaystyle \frac{1}{2}\left(\sqrt{2}\right)(2)\sin\theta \:=\:1 \quad\Rightarrow\quad \sin\theta \:=\:\frac{1}{\sqrt{2}} \quad\Rightarrow\quad \theta \:=\:45^o$

Hence, the triangle looks like this:

The right half is identical to the left half.

Code:

*
* | *
_ * | * _
√2 * |1 * √2
* | *
* 45° | 45° *
* * * * * * * * *
1 1

Therefore, the triangle is an isosceles right triangle.