Hello!
The answer is:
The length of "x" is equal to 4 units.
Why?
To solve the problem and find the length of x, we need to remember the alternate angles rule. The alternate angles rule establish that alternate angles will be also equal.
So, for the triangles, we have:
The angle((α)) formed between the base (2.5) and the hypotenuse (5) of the big triangle is equal to the angle(α) formed between the base (2) and the hypotenuse (x) of the small triangle. It also means that the triangles are similar since they have congruent angles(α) and proportional sides (SAS).
We are given:
First triangle,
[tex]AdjacentSide=2.5\\Hypotenuse=5\\[/tex]
Second triangle,
[tex]AdjacentSide=2\\Hypotenuse=x\\[/tex]
So, using the cosine identity, we have:
[tex]Cos(\alpha)=\frac{AdjacentSide}{Hypotenuse}[/tex]
[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}[/tex]
[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}\\\\\frac{2.5}{5}=\frac{2}{x}\\\\x=2*\frac{5}{2.5}=4[/tex]
Therefore, we have that the hypotenuse of the second triangle (x) is equal to 4 units.
Hence, the length of "x" is equal to 4 units.
Have a nice day!
