B= b= \,\,(\sqrt[3]{36}) ^3 ( 3 36 ) 3

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

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Simplify the following expression: (−3)(−2)( −2) A −12 B 12 C −18 D 18

nydimaria [60]

A -12 Hope this helps

7 0

3 years ago

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Pog help pog pog pog pog pog pog pog pog pog

Luda [366]

Answer:

POG

Step-by-step explanation:

poggers + poggers = POGCHAMP

7 0

3 years ago

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Giselle's youth club sells cookies to fund their trips and activities. Each year they need to earn $1,247 from selling cookies.

algol [13]

Price per box, P = $1.45 .

Money left, M = $1247 - $472.70 = $774.3 .

Let, number of boxes are x.

So,

$x = \dfrac{774.3}{1.45}\\\\x = 534\ boxes$

Therefore, they have to sell 534 more boxes.

Hence, this is the required solution.

6 0

3 years ago

The sum of three consecutive integers is 126..............

Rasek [7]

The three consecutive integers are: x, (x+1) and (x+2).
We can suggest this equation:
x+(x+1)+(x+2)=126
3x+3=126
3x=126-3
3x=123
x=123/3
x=41

x=41
(x+1)=41+1=42
(x+2)=41+2=43

Answer: the three consecutive integers would be: 41,42 and 43.

6 0

3 years ago

B= b= \,\,(\sqrt[3]{36}) ^3 ( 3 36 ​ ) 3

B= b= \,\,(\sqrt[3]{36}) ^3 ( 3 36 ) 3