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Elanso [62]
3 years ago
10

What is the area of this triangle? (Image Attached)

Mathematics
2 answers:
Snezhnost [94]3 years ago
6 0
\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\
-----------------------------\\\\
\textit{so, let's find the missing side}
\\\\\\
c=\sqrt{2.7^2+3.4^2-2(2.7)(3.4)cos(40^o)}
\\\\\\
c=\sqrt{4.78542402433556327368}\implies c\approx 2.187561204706182220

or we can round it, to say c = 2.19, so  hmm that's the missing side
now, we use Heron's Formula, which uses all 3 sides only

\bf \textit{Heron's Area Formula}\\\\
A=\sqrt{s(s-a)(s-b)(s-c)}\qquad 
\begin{cases}
a=2.7\\
b=3.4\\
c\approx 2.19\\\\
s=\cfrac{a+b+c}{2}
\end{cases}

and that'd be the area of it
ratelena [41]3 years ago
4 0

Answer:

The area of the triangle is 2.97 ft².

Step-by-step explanation:

We are given the triangle having sides 2.7 feet, 3.4 feet and the inclusive angle 40°.

We will find the length of the third side.

The law of cosines is given by c^{2}=a^{2}+b^{2}-2ab\cos \theta.

Substituting the values, we have,

c^{2}=2.7^{2}+3.4^{2}-2\times 2.7\times 3.4\cos 40\\\\c^{2}=7.29+11.56-18.36\times 0.766\\\\c^{2}=18.85-14.06\\\\c^2=4.79\\\\c=2.2

Thus, the length of the third side is 2.2 feet.

Now, the Heron's Area Formula is given by A=\sqrt{s(s-a)(s-b)(s-c)}, where s=\frac{a+b+c}{2}.

So, s=\frac{2.7+3.4+2.2}{2}\\\\s=\frac{8.3}{2}\\\\s=4.15

Then, the area of the triangle is,

A=\sqrt{4.15(4.15-2.7)(4.15-3.4)(4.15-2.2)}\\\\A=\sqrt{4.15\times 1.45\times 0.75\times 1.95}\\\\A=\sqrt{8.80059375}\\\\A=2.97

<h3>Thus, the area of the triangle is 2.97 ft².</h3>
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X^2-4x+c find the value of c
Sonbull [250]

Answer:

c = 4

Step-by-step explanation:

Given

x^2 - 4x + c

Required

Find c

The question is incomplete. However, I'll assume the expression is a perfect square.

To find c, we make use of the following formula

c = (\frac{b}{2})^2

Where

ax^2 + bx + c

By comparison with x^2 - 4x + c

a =1

b = -4

So, c = (\frac{b}{2})^2 becomes

c = (\frac{-4}{2})^2

c = (-2)^2

c = 4

<em>The value of c that makes the expression, </em>x^2 - 4x + c<em> a perfect square is 4 and the expression is: </em>x^2 - 4x + 4<em></em>

8 0
2 years ago
Movies are on sale for 3/4 the original price. If the original price is $16, what is the sale price?
Nesterboy [21]

If the original price is 16, then 3/4 of 16 is 12.

$12


Dividing 16 by 4 (the denominator), you get 4. Then 4 x 3 (the numerator) is 12.

5 0
3 years ago
Para decorar una pared se disponen de tiras de papel azules de 15 cm, verdes de 20 cm, y rojas de 25 cm. En la pared se quiere a
den301095 [7]

Answer:

a) Smallest line that can be made with each color = 300 cm

b) Total strips should be used = 47 strips

c) Total strips used of blue color = 20

  Total strips used of green color = 15

  Total strips used of red color = 12

Step-by-step explanation:

Given - To decorate a wall, there are 15 cm blue, 20 cm green, and 25 cm red strips of paper. On the wall you want to build three lines of the same size, one of each color and without cutting any strip.

To find - a) How long is the smallest line that can be made with each color?

              b) How many strips should be used?

              c) How many of each color?

Proof -

a)

For the smallest line that can be made with each color, we just have to find the lcm (least common multiple) of the 3 srtips.

Firstly,

Decompose the 3 strips to its prime factors , we get

15 = 3×5

20 = 2²×5

25 = 5²

So,

The Lcm(15, 20, 25) = 3×2²×5² = 3×4×25 = 300

∴ we get

Smallest line that can be made with each color = 300 cm

b)

Now,

Total strips used = 300 cm

Strips used by 15 cm blue = \frac{300}{15} = 20 strips

Strips used by 20 cm green = \frac{300}{20} = 15 strips

Strips used by 25 cm red = \frac{300}{25} = 12 strips

So,

Total strips should be used = 20 + 15 + 12 = 47 strips

c)

Total strips used of blue color = 20

Total strips used of green color = 15

Total strips used of red color = 12

6 0
2 years ago
Find the length of side x in simplest radical form with rational denominator.
DaniilM [7]

Answer:

sqrt(20)

Step-by-step explanation:

The two perpendicular side lengths are equal, so using Pythagoras theorem:

x = sqrt( sqrt(10)^2 + sqrt(10)^2 )

x = sqrt(10 + 10)

x = sqrt(20)

8 0
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Oh my gosh help me i
Ivanshal [37]

Sorry its hard to read and see

4 0
3 years ago
Read 2 more answers
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