1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Advocard [28]
2 years ago
14

An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length

of 5 centimeters. The apothem and radius form a triangle with a base length of b. Which statements about finding the area of the equilateral triangle are true? Select three options

Mathematics
1 answer:
Anna007 [38]2 years ago
8 0

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 centre 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.

You might be interested in
Help me on this math promblem it’s also a missing and is effecting me
Vlad1618 [11]

Answer:

$20.42

Step-by-step explanation:

Given that:

Price of tablet computer = $255.25

Sales tax = 8%

Sales tax will be calculated as follows:

tax amount = 0.08 (255.25)

tax amount = $20.42

So Azim will spend $20.42 on the sales tax.

i hope it will help you!

4 0
3 years ago
yuson must complete 30 hours of community service. she does 2 hours each day. which linear equation represents the hours yuson h
algol [13]

Answer:

30-2x

Step-by-step explanation:

yuson has to finish am total of 30 hours in community service

she does 2 hours each day

in x days, hour of service done=2x

after x days hours of service left=30-2x

therefore the linear equation representing the hours yuson has left after x days is:

30-2x

6 0
2 years ago
To create an entry​ code, you must first choose 2 letters and​ then, 4 ​single-digit numbers. How many different entry codes can
Murrr4er [49]
Assuming that the letters can only be capitals or non-capitals then:
(26P2)*(9P1)*4 = 23400 possible combanations 
8 0
3 years ago
What is the true solution to the equation below?
jarptica [38.1K]

Answer:

Step-by-step explanation:

some rules of logarithmic function

ln(a) - ln(b)=ln(\frac{a}{b})

e^{ln(a)}=a

ln(a)^{n}=nln(a) vice-versa nln(a)=ln(a)^{n}

If ㏑(a) = ㏑(b), then a = b

∴ 2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)

Use the 2nd rule to simplify it

e^{ln(2x)}=2x\\e^{ln(10x)}=10x\\

2㏑(2x) - ㏑(10x) = ㏑(30)

Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})\\\\ln(\frac{4x^{2}}{10x})=ln(30)\\\\ \frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x\\\\ ln(\frac{2}{5}x)=ln(30)

Use the 4th rule

\frac{2}{5} x = 30

Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

3 0
3 years ago
7 more than 11 times a number increased by the quotient of y and z
umka21 [38]
11(x)+y/z+7


........
..........................
5 0
3 years ago
Read 2 more answers
Other questions:
  • GIVING BRAINLIEST<br><br> Graphing required <br><br><br><br> Answer ASAP
    6·1 answer
  • Tan (angle B) using an exact expression in trigonometric ratios in right triangles
    12·1 answer
  • A group of hikers are 675 ft from the base of Guadalupe Peak, which is 8,749 ft tall. What is the angle of elevation when they l
    11·1 answer
  • If ∠ECD = 45° and ∠BED = 110° is ΔABE ~ ΔCDE? If so, by what criterion? A) yes, by AA criterion B) yes, by SAS criterion C) yes,
    14·2 answers
  • 2 factions have the same numerator but different denominator . is the fraction with the greater denominator greater or less than
    8·1 answer
  • What is the exact area of a circle with a diameter of 18 feet?
    7·1 answer
  • - Ashanti earns $50 an hour. How much does she earn in 6 hours?
    5·1 answer
  • Toni decided to build a rectangular concrete patio 6 feet wide all around her pool.
    9·1 answer
  • Please help me fastttt!!!!
    15·1 answer
  • Polynomial factoring: <br> 2x^4 + x^2- 6
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!