How to find the area of an equilateral triangle inside a circle

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now, from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

The statements that are true for the considered equilateral triangle are:

For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.

For this case, referring to the figure attached below, we have:

Since the triangle is equilateral, there can be 6 congruent triangles like BOD.

Thus, Area of triangle ABC = 6 × Area of triangle BOD

Area of BOD = [tex]\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2[/tex]

Area of ABC = [tex]6 \times 2.175x = 13.05x \: \rm cm^2[/tex]

The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.

We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).

[tex]tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm[/tex]

Using Pythagoras theorem too, we can get the value of x as:

[tex]5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm[/tex]

Thus, area of the equilateral triangle ≈ [tex]13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2[/tex]

This isn't 65 sq. cm.

Thus, the statements that are true for the considered equilateral triangle are:

Learn more about tangent ratio here:

https://brainly.com/question/14169279

Answer:

x ≈ 23.31

Step-by-step explanation:

We can use the law of cosines because we know 2 sides and 1 angle.

The general formula  for the law of cosines if the triangle sides are a, b,c and α is the angle between sides a and b. c is the missing side.

[tex]c = \sqrt{a^{2} +b^{2} -2*a*b* cos \alpha }[/tex]

In our problem the law of cosines is

x = [tex]\sqrt{21^{2} +13^{2} - 2*21*13 *cos 83}[/tex]

x ≈ 23.31

Answer:

all angles are congruent

Answer:

[tex]2.4x-4.4[/tex]

Step-by-step explanation:

Given the following question:

[tex]0.3(4x-8)-0.5(-2.4x+4)[/tex]

To simplify the expression, we are going to need to rewrite the expression by expanding the terms and then solve by using the distributive property. Then we combine like terms in till the expression can no longer be simplified to find our answer.

[tex]0.3(4x-8)-0.5(-2.4x+4)[/tex]
[tex]0.3(4x-8)[/tex]
[tex]0.3\times4=1.2x[/tex]
[tex]0.3\times4=2.4[/tex]
[tex]1.2x-1.2-0.5(-2.4x+4)[/tex]
[tex]-0.5(-2.4x+4)[/tex]
[tex]-0.5\times-2.4=1.2[/tex]
[tex]-0.5\times4=-2[/tex]
[tex]1.2-2[/tex]
[tex]1.2x-2.4+1.2x-2[/tex]
[tex]1.2+1.2=2.4x[/tex]
[tex]-2.4+-2=-4.4[/tex]
[tex]=2.4x-4.4[/tex]

Your answer is "2.4x - 4.4."

Hope this helps.

Answer:

1. Z-24 < 12

2. A-12.65 ≤ 26,000

3. Z-999 < 500

4. -10x ≥ 25

5. f - -1 < 0 or f+1 < 0

6. y/14 ≥ 0.5

Answer:

[tex]-3m-2k[/tex]

Step-by-step explanation:

Given to simplify : 3k - (2m + 5K) - m

Solution :

[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]

[tex]-\left(2m+5k\right)=-2m-5k[/tex]

[tex]=3k-2m-5k-m[/tex]

[tex]\mathrm{Group\;like\;terms}[/tex]

[tex]=-2m-m+3k-5k[/tex]

[tex]\mathrm{Group\;like\;terms}[/tex]

[tex]=-3m+3k-5k[/tex]

[tex]\mathrm{Group\;like\;terms}[/tex]

[tex]=-3m-2k[/tex]

[RevyBreeze]

Use the distributive property:-

-(2m+5k) = -2m-5k [tex]\checkmark[/tex]

[tex]\rule{270}{1}[/tex]

Let's simplify this expression by combining like terms:-

[tex]\bigstar[/tex] The like terms are:-

3k, -5k

and

-2m, -m

[tex]\bigstar{[/tex] Combine Like terms:-

3k-5k=-2k

-2m-m=-3m

Hence, we have:-

[tex]\bigstar{\boxed{\pmb{-2k-3m}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

the answer is 2.5%

Step-by-step explanation:

im good at math

Hope this helps!

The possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

It should be noted that a persuasive speech simply means a speech that is used to convince an individual to agree to a particular perspective.

In this case, the possible next step that Annie should use in the persuasive speech is to discuss the lack of street lamps and campus security as causes of the problem.

Learn more about speech on:

https://brainly.com/question/25887038

Answer:

$5.80

Step-by-step explanation:

butterscotch + milk

butterscotch:

$1/5 = $0.20 x 4 = $0.80

milk:

$1 x 5 = $5

$5 + $0.80 = $5.80

Answer:

5:6

Step-by-step explanation:

To find the ratio of side lengths you need to cube root of the ratio of the volumes. The reason you use the cube root is because you are multiplying 3 things together when you find volume.

[tex]\sqrt[3]{\frac{125}{216} } =\frac{5}{6}[/tex]

5 : 6

Answer:

43.78

Step-by-step explanation:

In this case, the formula for mean can be as followed:

[tex]mean = \frac{sum \: of \: all \: student \: scores}{number \: of \: students} [/tex]

Let the sum of all student scores for class A and class B be A and B respectfully,

For Class A,

A/28 = 34

A/28 = 34A = 952

For Class B,

B/8 = 78

B/8 = 78B = 624

Now to find the mean score of both classes using the same formula,

Mean = (952+624)/(28+8)

= 43.77777777777778

≈ 43.78

Answer:

100

Step-by-step explanation:

10^3= 10x10x10= 1000

10^4= 10x10x10x10= 10000

10^5= 10x10x10x10x10= 100000

( the quickest way to sove this is by add 0 behind the one, whatever the exponent is, thats how many zeroes there abre going to be.

ex: 10^3 theres 3 exponents so theres going to be 3 zeroes behind the one

step 2 solve

1000x10000/100000= 100

Answer:

10^2

Step-by-step explanation:

10^3⋅10^4/10^5

add the exponents when multiplying

10^7/10^5

subtract the exponents when dividing

10^2

Answer:

Hence, the square root of 8 is not a rational number. It is an irrational number.

Step-by-step explanation:

according to my math book.. thanks me later

Answer:

(3,5)

Step-by-step explanation:

We first need to substitute x for 3 in the equation :)

y = 2(3) - 1

y = 6 - 1

y = 5

The cordinate will be (3,5)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

i think the surface would be 2

Answer:

x=8.4

i looked it up:)

Answer:

the answer to the graph is y=-4x-3

Answer:

y = -4x - 3

Step-by-step explanation:

The given line has :-

Substituting in slope-intercept form

Step-by-step explanation:

3x + 4 + 2x +7

= 3x + 2x + 4 + 7

= 5x + 11

Answer: 24

Step-by-step explanation:

Corresponding sides of similar figures are proportional.

Answer:

11.72

Step-by-step explanation:

6.76 + 4.96 = 11.72

Answer: 110 degrees

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees, so the third angle is 180-40-30=110 degrees.

TSA:-

Answer:

D. [tex]\displaystyle No\:Solution[/tex]

Explanation:

The absolute value of an integer is NEVER negative, hence, your answer. ON THE OTHER HAND, these are the only exceptions:

[tex]\displaystyle -6 = -|3[-2]| \\ -6 = -|3[2]|[/tex]

The negative absolute value of an integer however, IS negative.

I hope you are capable of differentiating between the two, and as always, I am joyous to assist anyone at any time.

Answer:

18h × 6g is equivalent to 6(3h + g)

because 6 x 3 = 18 and 6 x 1 = 6

Answer:

B, 20

Step-by-step explanation:

The Pythagorean Theorem states that the two shortest lengths in a right triangle (in our case, 12 and 16), is equal to the longest length in a right triangle (c). So,

a²+b²=c²

Substitute 12 and 16 for a and b, our side lengths

12²+16²=c²

144+256=400

400=c²

Square root both c and 400, which gives us...

20=c

So, the value of x is 20.

Answer:

is this a multiple choice question? if so can you retype it out to show the separate answer choices because im having trouble reading your question.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Took the test and got it right.

Answer:

B: 6 miles

Step-by-step explanation:

You divide 18 by 3 and get 6.

Answer:

hello, i am not sure. but the answer is between a and c

Step-by-step explanation:

[tex](x - 3)(2x {}^{2} - 5x + 1)[/tex]

[tex]2x {}^{3} - 5x {}^{2} + x - 6x {}^{2} + 15x - 3 [/tex]

[tex]2x {}^{3} - 11x {}^{2} + 16x - 3[/tex]

Answer:

13

Step-by-step explanation:

7j=91

91/7=j

13

hope that helps:)