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KATRIN_1 [288]
2 years ago
9

need answers to these two questions with work, must find the measurement indicated using the law of sines. round answer to the n

earest tenth.

Mathematics
1 answer:
sweet [91]2 years ago
5 0

Applying the law of sines, the measurement indicated are:

7. AB = 24.1 cm

8. BC = 28.0 in.

<h3>What is the Law of Sines?</h3>

Law of sines is: sin A/a = sin B/b = sin C/c.

7. AB (c) = ?

BC (a) = 22 cm

A = 180 - 138 - 22 = 20°

C = 22°

Apply the law of sines:

sin 22/AB = sin 20/22

AB = (sin 22 × 22)/sin 20

AB = 24.1 cm

8. BC (a) = ?

A = 58°

AC (b) = 33 in.

B = 180 - 58 - 33 = 89°

Apply the law of sines:

sin 58/BC = sin 89/33

BC = (sin 58 × 33)/sin 89

BC = 28.0 in.

Learn more about the law of sines on:

brainly.com/question/2807639

#SPJ1

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The area of a rectangle is 72cm square. Length,/, of the rectangle is 6 cm longer than the width w
Butoxors [25]
As you haven't specifically stated what exactly the question is, I will be assuming that the question is most likely asking for what the dimensions ( length and width ) of the rectangle is. With this in mind, I will be answering the question so here I go...


STEP-BY-STEP SOLUTION:

Let's solve this problem step-by-step.

Let's first establish the formula for the area of a rectangle as displayed below:

Area = Length × Width

A = lw

From this, we will establish the values for each of the parts in the area formula using the information given in the problem as displayed below:

A = 72cm^2

l = w + 6

w = w

Now, we will substitute these values into the area formula and then make ( w ) the subject as displayed below:

A = lw

72 = ( w + 6 ) ( w )

72 = w ( w + 6 )

72 = w^2 + 6w

0 = w^2 + 6w - 72

0 = w^2 + 12w - 6w - 72

0 = w ( w + 12 ) - 6 ( w + 12 )

0 = ( w + 12 ) ( w - 6 )


w + 12 = 0

w = 0 - 12

w = - 12


w - 6 = 0

w = 0 + 6

w = 6

As the answer must be positive as measurements are always positive, the answer must be the option which is a positive number.

Therefore:

w = 6

Using the equation we made for the length before, we can substitute the value of ( w ) to obtain the value of the length as displayed below:

l = w + 6

l = ( 6 ) + 6

l = 12


FINAL ANSWER:

The dimensions of the rectangle are:

Length = 12cm

Width = 6cm


Please mark as brainliest if this was helpful! : )
Thank you <3
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Step-by-step explanation:

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