Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

Mathematics

1 answer:

Katena32 [7]3 years ago

7 0

The area of an equilateral triangle is $9\sqrt{3} /4$

<u>Step-by-step explanation:</u>

Perimeter of a triangle = 3a

⇒ 9 = 3a

⇒ a = 9/3

a = 3

Area of an equilateral triangle = $\sqrt{3}/ 4\times a^{2}$

⇒ $\sqrt{3}/ 4\times 3^{2}$

⇒ $\sqrt{3}/ 4\times 9$

⇒ $9\sqrt{3} /4$

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two observers, Anna and Bryan. sight a kite at angles 44 degrees and 66 degrees. respictively. if anna is located 20m from the k

Arada [10]

Answer:

28.6m

Step-by-step explanation:

this question is very incomplete. it requires a number of assumptions to give an answer. the main one - where is Bryan located relative to Anna ? I assume diametrically on the opposite side of the kite. because he has the steeper angle, it is clear that he is nearer to the kite.

so, I guess, we have to add his distance to the kite to her distance to the kite to get the distance between her and him.

but he could be on any point on a circle around the kite to have the same viewing angle, and we would have no clue about where on that circle.

as the other extreme alternative, he could be on the same line to the kite as Anna. and then we would have to subtract his distance from her distance.

but again, we assume he is exactly on the other side of the kite.

anyway, each person creates a right-angled triangle with the kite:

there is the direct line of sight as the base line or Hypotenuse (c).

there is the line on the ground from the person to the point on the ground directly under the kite as one side.

there is the line representing the height of the kite above ground as the other side. we let this start at the height of the eyes of the watching person.

and we assume that both persons are of the same height (so the height of the kite relative to their eyes is the same for both).

let's start with Anna.

the side a of Anna's triangle is

a = 20m

angle between a and c = 44 degrees

we know the angle between a and b is 90 degrees.

therefore the angle between b and c = 180-90-44 = 46 degrees.

now we use the law of sines :

a/sin(bc) = b/sin(ac) = c/sin(ab)

we know sin(ab) = sin(90) = 1

20/sin(46) = b/sin(44)

b = 20×sin(44)/sin(46) = 19.31... m = height of the kite