Which is equivalent to 4 square root 9^1/2^?

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

A bakery sold a total of 300 cupcakes in a day, and 252 of them were chocolate flavored. what percentage of cupcakes sold that d

mars1129 [50]

Answer:

84% of the cupcakes were chocolate- flavored.

Step-by-step explanation:

$\frac{252}{300} = \frac{84}{100} = 84\%$

4 0

1 year ago

Cari knows that a certain species of fish need 240 cubic feet of water in their tank.the tank has a height of 12 feet and a widt

pochemuha

The equation that can be used to find the length of the tank is 240 = l × 12 × 10

<h3>How to find the volume of rectangular prism?</h3>

The volume of a rectangular prism can be found as follows:

volume of rectangular prism = lwh

where

l = length
w = width
h = height

Therefore,

volume of rectangular prism = lwh

volume of rectangular prism = 240 ft³

h = 12 ft

w = 10 ft

Therefore, the let's find the length of the tank.

240 = l × 12 × 10

240 = 120l

divide both sides by 120

l = 240 / 120

l = 2

learn more on volume here:brainly.com/question/21308574

#SPJ1

8 0

1 year ago

Simplify the following, leaving your answer with a positive exponent: <br> x^-12/ x^-7

storchak [24]

Answer:

$\frac{1}{x^{5} }$

Step-by-step explanation:

x^-12/ x^-7

= x^(-12-(-7))

= x^-5

= 1/x^5

3 0

3 years ago

The expression for the distance traveled is rt where r represents rate and t represents time.

astraxan [27]

I don't really get what the "35,000 feet university sea level" part is saying, but without it, the answer would be:

3.5 x 550 = 1,925

The plane traveled 1,925 miles.

And with it, the answer would be:

3.5 x 550 = 1,925

35,000 ft = 6.6 mi

1,925 + 6.6 = 1,931.6

The plane traveled 1,931.6 miles.

Hope this helped a little at least.

8 0

3 years ago