Answer:
[tex]y= 7\sqrt{2}[/tex] units
Step-by-step explanation:
Using tangent ratio:
[tex]\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
As per the statement:
In the given right angle triangle.
First find x:
Using tangent ratio:
[tex]\tan 45^{\circ} = \frac{7}{x}[/tex]
[tex]1 = \frac{7}{x}[/tex]
⇒x = 7 units
We have to find the value of y:
Using Pythagoras theorem;
[tex]\text{Hypotenuse side}^2=\text{opposite side}^2+\text{Adjacent side}^2[/tex]
Substitute the given values we have;
[tex]y^2 = 7^2+7^2[/tex]
⇒[tex]y^2 = 49+49 = 98[/tex]
⇒[tex]y = \sqrt{98} = \sqrt{49 \cdot 2} = \sqrt{7^2 \cdot 2}[/tex]
⇒[tex]y = 7\sqrt{2}[/tex] units
Therefore, the value of y is, [tex] 7\sqrt{2}[/tex] units
