Find the lengths of the missing sides in the triangle write your answers as integers or as decimals

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 391 People

(2 points)
7. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals
rounded to the nearest tenth. The diagram is not drawn to scale.
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Answered by maham237 @ 22/12/2020

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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