Question

the length of the hypotenuse of a 30-60-90 triangle is 11 find the perimeter

Answer 1

The perimeter of the triangle is 21.2 units.

What is perimeter of triangle?

'The perimeter of a triangle is the total distance around the edges of a triangle.'

According to the given problem,

Hypotenuse = 11

θ = 30°

We know,

Sine30 = $\frac{length}{hypotenuse}$

⇒ 0.5 = $\frac{length}{hypotenuse}$

⇒ Length = 0.5 × 11

⇒ Length = 5.5

Cosθ = $\frac{Base}{Hypotenuse}$

⇒ Base = $\frac{\sqrt{3} }{2}$ × Hypotenuse

⇒ Base =     4.7

Perimeter = length + base + hypotenuse

                 = 5.5 + 4.7 + 11

                  =21.2

Hence, we can conclude, the perimeter of the triangle is 21.2 units.

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