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savannahvargas512

21.04.2022

Mathematics

The lengths of the missing sides in the triangle is x = 9.89 units & y = 7 units.

Step-by-step explanation:

In the given figure, it's a right angled triangle with sides as :

Perpendicular = 7 units

Base = y units

Hypotenuse = x units

Here, Tan $\alpha =$ $\frac{Perpencdicular}{Base}$ and , Tan45 ° = 1

⇒ Tan $\alpha =$ $\frac{Perpencdicular}{Base}$

⇒ Tan 45 = $\frac{7}{y}$

⇒ $1 = \frac{7}{y}$

⇒ y = 7

Now, by Pythagoras Theorem :

$Hypotenuse^{2} = Perpendicular^{2} + Base^{2}$

⇒ $x^{2} = y^{2} + 7^{2}$

⇒ $x^{2} = 7^{2} +7^{2}$

⇒ $x^{2} = 49 + 49 = 98$

⇒ $x = 7\sqrt{2} = 9.89 units$

∴ The lengths of the missing sides in the triangle is x = 9.89 units & y = 7 units.

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