Question

step by step explanation

Answer 1

Answer:

45 into 3√2

Step-by-step explanation:

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Answer 2

The area of the given triangle is $9units^{2}$.

The perimeter of the triangle is $6(1+\sqrt{2} )units$.

Given,

In ΔABC,

∠$B=90$°

∠$C=45$°

$AB=3\sqrt{2}unit$

To find,

1. Sides of the triangle.

2. Perimeter of the triangle.

3. Area of the triangle.

Solution,

Since ΔABC is a right-angled triangle,

Using trigonometric ratios,

$tan45=\frac{AB}{BC}$

⇒$1=\frac{3\sqrt{2} }{BC}$

⇒$BC=3\sqrt{2} units$

Similarly,

$sin45=\frac{AB}{AC}$

⇒$\frac{1}{\sqrt{2} }=\frac{3\sqrt{2} }{AC}$

⇒$AC=3\sqrt{2}\sqrt{2}$

⇒$AC=3(2)units$

⇒$AC=6units$

So,

The perimeter of ΔABC,

⇒$P=AB+BC+AC$

⇒$P=(3\sqrt{2}+3\sqrt{2}+6) units$

⇒$P=6+6\sqrt{2}units$

⇒$P=6(1+\sqrt{2} )units$

And, area

⇒$A=\frac{1}{2}.BC.AB$

⇒$A=\frac{1}{2}(3\sqrt{2} ) (3\sqrt{2} )$

⇒$A=\frac{1}{2} (9)(2)$

⇒$A=9units^{2}$

Therefore,

1.

The sides of the triangle are,

$AB=3\sqrt{2}units \\BC=3\sqrt{2}units \\AC=6units$

2.

The perimeter of the triangle is, $P=6(1+\sqrt{2} )units$.

3.

Area of the triangle, $A=9units^{2}$.