Question

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

Answer 1

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]

Answer 2

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.