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Bogdan [553]
3 years ago
13

Given an equilateral triangle with two vertices located at (-8, -5) and (3, 7), what is its perimeter?

Mathematics
1 answer:
Oduvanchick [21]3 years ago
7 0
An equilateral triangle has 3 sides of equal length
find the length of 1 side and that is the length of te other 2 sides
so find the length and times 3

we need to find the distance betwen the points (-8,-5) and (3,7)

distance between the points (x1,y1) and (x2,y2) is
D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
so
distance between (-8,-5) and (3,7) is
D=\sqrt{(-8-3)^2+(-5-7)^2}
D=\sqrt{(-11)^2+(-12)^2}
D=\sqrt{121+144}
D=\sqrt{265}

the distance is √265
the perimiter is 3√265 units
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Step-by-step explanation:

The diagram of the triangle is shown in the attached photo. The triangle is a right angle triangle ABC

Assuming the given angle is #,

Recalling the trigonometric ratio,

tan # = opposite / adjacent

If tan # = 4, it means

opposite / adjacent = 4/1

Therefore, opposite = 4 and adjacent = 1

Applying Pythagoras theorem,

Hypotenuse^2 = opposite ^2 + adjacent ^2

Hypotenuse = AC

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AC^2 = 4^2 + 1^2 = 17

AC = ± √17

To determine cos #, we would apply another trigonometric ratio,

Cos# = adjacent /hypotenuse

Cos# = 1/±√17

Cos # =-1 /√17 or 1/√17

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