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3 years ago

In triangle ABC, a=31 , b=22 , c=18. Identify m∠A rounded to the nearest degree.

Mathematics

1 answer:

Veronika [31]3 years ago

8 0

Answer:

101

Step-by-step explanation:

According to the Law of Cosines, for any △ABC with side lengths a, b, and c, a2=b2+c2−2bccosA; b2=a2+c2−2accosB; and c2=a2+b2−2abcosC

The Law of Cosines can be used because all three side lentghs are known.

Set up the equation for the Law of Cosines:

a2=b2+c2−2bccosA

Substitute the known values into the Law of Cosines:

312=222+182−2(22)(18)cosA

Square the values and multiply:

961=484+324−792cosA

Add:

961=808−792cosA

Subtract 808

from both sides:

153=−792cosA

Divide both sides by −792

153−792=cosA

According to this equation m∠A

is equal to the inverse cosine function of −153792

. Write this:

m∠A=cos−1(−153792)

Calculate the value of the inverse cosine −153792

on a calculator:

m∠A≈101°

Therefore, m∠A≈101°

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BlackZzzverrR [31]

We will start off working on the right hand side.
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(cos x)^ 2 - (sin x)^2 = cos(2x) 
sin 2x = 2 sin x cos x 

Note that by arranging the second formula, we will have sin x cos x = (1/2) sin 2x 

Hence, we will get: 
[(cos x)^ 2 - (sin x)^2] / [sin x cos x] 
= [cos 2x] / (1/2)[sin 2x] 
= 2[cos 2x] / [sin 2x] 
= 2cot 2x

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3 years ago

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castortr0y [4]

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6 0

3 years ago

Read 2 more answers

After a storm damages the community center, Shanika and her friends hold fundraising

Inessa [10]

Answer:

The total amount of money Shanika and her friends want to raise is $2400.

Step-by-step explanation:

Given:

After a storm damages the community center, Shanika and her friends hold fundraising.

After the first event, they raise $240, which is 10% of the total amount that they want to raise.

Now, to find the total amount of money that Shanika and her friends want to raise.

Let the total amount of money that Shanika and her friends want to raise be $x$ .

As given 10% of fundraise is $240.

So, according to question:

$10\%\ of\ x=\$240.$

$\frac{10}{100}\times x=240$

$\frac{10x}{100}=240.$

Multiplying both sides by 100 we get:

$10x=24000.$

Dividing both sides by 10 we get:

$x=\$2400.$

Therefore, the total amount of money Shanika and her friends want to raise is $2400.

3 0

3 years ago

Please help right now!!!!! Solve the system of equations below. x + y = 7 2x + 3y = 16

motikmotik

Answer:

$x=5$ and $y=2$ .

Step-by-step explanation:

We have been given a system of equations. We are asked to solve our given system.

$x+y=7...(1)$

$2x+3y=16...(2)$

From equation (1), we will get:

$x=7-y$

Upon substituting this value in equation (2), we will get:

$2(7-y)+3y=16$

$14-2y+3y=16$

$14+y=16$

$14-14+y=16-14$

$y=2$

Now, we will substitute $y=2$ in equation (1).

$x+2=7$

$x+2-2=7-2$

$x=5$

Therefore, the point $(5,2)$ is solution for our given equation.

7 0

3 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Alekssandra [29.7K]

In the given figure we can determine the coordinate of point M from the graph, we get:

$M=(\frac{d}{2},\frac{c}{2})$

We can also determine the coordinates of point N as:

$N=(\frac{a+b}{2},\frac{c}{2})$

Now, to determine the length of segment MN, we need to subtract the x-coordinate of M from the coordinates of N, we get:

$MN=\frac{a+b}{2}-\frac{d}{2}$

Subtracting the fractions we get:

$MN=\frac{a+b-d}{2}$

Now, to obtain the length of AB we need to subtract the x-coordinate of A from the x-coordinate of B.

The coordinates of A are determined from the graph:

$A=(0,0)$

The coordinates of B are:

$B=(a,0)$

Therefore, the length of segment AB is:

$AB=a$

Now we do the same procedure to determine the segment of CD. The coordinates of C are:

$C=(b,c)$

The coordinates of D are:

$D=(d,c)$

Therefore, CD is:

$CD=b-d$

Now, we determine MN as half the sum of the bases. The bases are AB and CD, therefore:

$MN=\frac{1}{2}(a+b-d)$

Therefore, we have proven that the median of a trapezoid equals half the sum of its bases.

8 0

1 year ago