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Harrizon [31]
3 years ago
7

What is the perimeter of a 30°-60°-90° triangle that has a long leg of 9?

Mathematics
2 answers:
saul85 [17]3 years ago
6 0

Answer:

21.29 units

Step-by-step explanation:

30° 60° 90° triangles have a specific side ratio.

With respect to side a, x is side a, x√3 is side b, and 2x is side c.

Therefore the perimeter is the sum of these sides.

c is the long side so:

9 = 2x. x = 9/2 = 4.5.

x√3 = 4.5√3 ≈ 4.5 × 1.73 ≈ 7.79.

Perimeter = x + x√3 + 2x =

(9/2) + (9/2)√3 + 9 = 4.5 + 7.79 + 9 = 21.29.

_______________________________

Exact answer: (27 + 9√3) / 2

Decimal: 21.29 [Nearest hundredth]

Helga [31]3 years ago
4 0

GIVEN:

  • b = 9
  • α = 30°
  • β = 60°
  • γ = 90°

TO FIND:

  • a = ?
  • c = ?

ANSWER:

On using trigonometric function,

Then, tan(30°) = a/b

a = tan(30°)b

  • 3⋅√3

And, cos(30°) = b/c

c = bcos(30°)

  • 6⋅√3

So, Perimeter of Δ = 9 + 6√3 + 3√3

  • 9 + 9√3
  • 9(1 + √3)

NOTE: See picture attached.

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