Q. 35.0( 1 Vote )

# Calculate the perimeter of the triangle shown below.

Answer :

__We know that sum of angles of a triangle is 180°.__

⇒ ∠A + ∠B + ∠C = 180°

⇒ 30° + 105° + ∠C = 180°

⇒ ∠C = 180° - 135°

∴ ∠C = 45°

We know that the sine rule is = =.

In the triangle above, we have

⇒ c = 2 m;

a, b =?

Consider

∴ a = √2 ≈ 1.41 m

Now consider = ,

⇒ b

= √3 + 1

∴ b = √3 + 1 ≈ 1.73 + 1 = 2.73 m

__We know that perimeter of a polygon is the sum of all its sides.__

∴ Perimeter = a + b + c

= 1.41 + 2.73 + 2

= 6.14 m

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