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LenKa [72]
3 years ago
11

Hunter wants to draw an obtuse equilateral triangle, but hes's having trouble drawing it. Is sush a triangle possible to draw? E

xplain your reasoning.
Mathematics
1 answer:
zavuch27 [327]3 years ago
7 0

let's recall that the sum of all interior angles in a triangle is 180°.

an equi-lateral, equal sides, triangle has all sides that are equal.

sides that are equal will yield an equal opposite angle.

so if all sides are equal, all angles are equal, for a sum of 180°, that's only possible with 60°, 60° and 60° angles, and all of them are acute, none obtuse.

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Given:

Universal set = {a, b, c, d, e, f, g, h}

A = {a, b, c, d}

B = {a, d, e}

C= {c, f, g, h}

To find:

The elements of set B'.

Solution:

Let universal set be U.

U = {a, b, c, d, e, f, g, h}

We know that,

Compliment of a set = Universal set - Set

It means,

B'=U-B

B'=\{a, b, c, d, e, f, g, h\}-\{a,d,e\}

B'=\{b, c,f, g, h\}

Therefore, only b, c, f, g, h are the elements of set B'.

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In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
sergiy2304 [10]

Given:

In triangle ABC, AC=13, BC=84, AB=85.

To find:

The measure of angle C.

Solution:

Law of Cosines:

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\cos C=\dfrac{BC^2+AC^2-AB^2}{2(BC)(AC)}

Substituting the given values, we get

\cos C=\dfrac{(84)^2+(13)^2-(85)^2}{2(84)(13)}

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\cos C=\dfrac{0}{2184}

\cos C=0

Taking cos inverse on both sides, we get

C=\cos^{-1}(0)

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Therefore, the measure of angle C is 90 degrees.

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