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2 years ago

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

Mathematics

2 answers:

saul85 [17]2 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]2 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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Using transformations and congruency concepts, it is found that with these following transformations, the triangles will be congruent.

A reflection, then a translation.
A rotation, then a reflection.

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Two triangles are congruent if they have the same lengths of the sides and the same angles.

In a reflection, there is a rule that changes the coordinates (x,y), but does not change the lengths of the sides of the triangles, thus they will still be congruent.
A reflection is also a special case of rotation, thus, in a rotation, the triangles are also congruent.
A translation is also similar to a reflection, using rules to shift the triangle up, down, left or right according to it's coordinates, not changing the sides or angles, thus congruent.
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Thus, from the bullet points above, the correct options are:

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A similar problem is given at brainly.com/question/24267298

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3 years ago

Construct a 95% confidence interval to estimate the population mean using the data below. x overbarequals37 sigmaequals10 nequa

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Answer:

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degree of freedom = n - 1 = 44 - 1 = 43

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Upper limit = mean + E = 37 + 3.04 = 40.04

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