Translate the phrase into a math expression 12 less than twice a number

Match each value with its formula for ABC.

MariettaO [177]

The solution to the question is:

c is 6 = $\sqrt{a^{2} + b^{2} -2abcosC }$

b is 5 = $\sqrt{a^{2} + c^{2} -2accosB }$

cosB is 2 = $\frac{a^{2} + c^{2} - b^{2} }{2ac}$

a is 4 = $\sqrt{b^{2} + c^{2} -2bccosA }$

cosA is 3 = $\frac{b^{2} + c^{2} -a^{2} }{2bc}$

cosC is 1 = $\frac{b^{2} + a^{2} - c^{2} }{2ab}$

<h3>What is cosine rule?</h3>

it is used to relate the three sides of a triangle with the angle facing one of its sides.

The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.

Analysis:

If c is the side facing the included angle C, then

$c^{2}$ = $a^{2}$ + $b^{2}$ -2ab cos C-----------------1

then c = $\sqrt{a^{2} + b^{2} -2abcosC }$

if b is the side facing the included angle B, then

$b^{2}$ = $a^{2}$ + $c^{2}$ -2accosB-----------------2

b = $\sqrt{a^{2} + c^{2} -2accosB }$

from equation 2, make cosB the subject of equation

2ac cosB = $a^{2}$ + $c^{2}$ - $b^{2}$

cosB = $\frac{a^{2} + c^{2} - b^{2} }{2ac}$

if a is the side facing the included angle A, then

$a^{2}$ = $b^{2}$ + $c^{2}$ -2bccosA--------------------3

a = $\sqrt{b^{2} + c^{2} -2bccosA }$

from equation 3, making cosA subject of the equation

2bcosA = $b^{2}$ + $c^{2}$ - $a^{2}$

cosA = $\frac{b^{2} + c^{2} -a^{2} }{2bc}$

from equation 1, making cos C the subject

2abcosC = $b^{2}$ + $a^{2}$ - $c^{2}$

cos C = $\frac{b^{2} + a^{2} - c^{2} }{2ab}$

In conclusion,

c is 6 = $\sqrt{a^{2} + b^{2} -2abcosC }$

b is 5 = $\sqrt{a^{2} + c^{2} -2accosB }$

cosB is 2 = $\frac{a^{2} + c^{2} - b^{2} }{2ac}$

a is 4 = $\sqrt{b^{2} + c^{2} -2bccosA }$

cosA is 3 = $\frac{b^{2} + c^{2} -a^{2} }{2bc}$

cosC is 1 = $\frac{b^{2} + a^{2} - c^{2} }{2ab}$

Learn more about cosine rule: brainly.com/question/4372174

$SPJ1

4 0

2 years ago

What is the surface area of the triangular prism (Look at image)

8_murik_8 [283]

Answer:

$\Large \boxed{\sf 384 \ m^2}$

Step-by-step explanation:

Surface area ⇒ area of 2 triangles + area of 3 rectangles

$(8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384$

3 0

3 years ago

Read 2 more answers

What is the answer?

iVinArrow [24]

Answer:42

Step-by-step explanation:

7 0

3 years ago

The workers at Cameron's Flower shop are putting 1,323 flowers into vases for a party .Each base must hold exactly 8 flowers .Wh

Alika [10]

Answer:

165

Step-by-step explanation:

How many complete vases can Cameron's Flower shop fill with 8 flowers each, considering they have a total of 1,323 flowers in total.

All you have to do is divide 1,323 by 8 to get = 165.375 or 165 and 3/8.

Since the question is about COMPLETE vases of 8 flowers, that means the answer is 165, and we don't count the 3 remaining flowers.

Good job Cameron!

3 0

3 years ago

Read 2 more answers

5lb 7oz -11oz need help quick

Aliun [14]

Answer:

76 ounces

Step-by-step explanation:

I'm assuming you meant:

5lb+7oz-11oz=

16 ounces in a pound

5lb+7oz-11oz=

80+7-11=

87-11=

76 ounces

3 0

3 years ago