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AlexFokin [52]
3 years ago
11

Find the area of the figure.( sides meet at right angles.)picture below

Mathematics
1 answer:
Tema [17]3 years ago
5 0

You can divide the figure as follows:

  • A vertical rectangle, 5 meters tall and 2 meters wide, on the top right.
  • A horizontal rectangle, 2 meters tall and 5 meters wide, on the bottom left
  • A 2x2 meters square on the bottom right, where the two rectangles meet.

The area of the rectangles is 5x2=10 meters squared, while the area of the square is 2x2=4 meters squared.

So, the total area is 10+4=14 meters squared.

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Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to
bekas [8.4K]

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

cos B= (a^2 + c^2 - b^2)/2ac

cos C = (a^2 + b^2 - c^2)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s^2 + s^2 - s^2)/(2s×s)

cos A = (s^2 )/(2s^2)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s^2 + s^2 - s^2)/(2s×s)

cos C = (s^2 )/(2s^2)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here: brainly.com/question/2866347

#SPJ1

3 0
1 year ago
a group of 4 pupils can take 2 weeks to do a certain job.how long will 12 pupils take to complete the job if they work at the sa
Ksivusya [100]

Answer:

6 weeks

Step-by-step explanation:

Set up a proportion where x is the amount of time with 12 pupils:

\frac{4}{2} = \frac{12}{x}

Cross multiply and solve for x:

4x = 24

x = 6

So, it will take 12 pupils 6 weeks to complete the job.

7 0
2 years ago
Lori rented a booth at the craft fair for $200 to sell baskets she made. The cost of the materials for each basket was $8. Lori
anastassius [24]

Answer:

15 baskets

Step-by-step explanation:

7 0
3 years ago
Shane and his family go to the movie theatre and buys 6 tickets for $12 each. then they spend a total of $31 for popcorn and dri
Bond [772]
I hope this helps you

3 0
2 years ago
How do I find the missing side?
SpyIntel [72]

Answer:

using pythagorean theorem I got that x=8.67698104181

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