1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
damaskus [11]
3 years ago
6

Find the value of b. Round the nearest tenth.

Mathematics
1 answer:
maria [59]3 years ago
3 0

Answer:

b= sin(43°) * 8 / sin(55°) ≈ 6.7

Step-by-step explanation:

Regarding the law of sines, each angle corresponds to the side opposite of it. Here, that means that the 82 degree angle is opposite of side c (so they correspond) and that the 55 degree angle corresponds to the side with 8cm. However, we are trying to find the length of side b. Therefore, assuming that the side with 8cm is side A, if we know that

sin A / a = sinB/b = sin C / C

= sin(55°)/8 = sinB/b = sin(82°) / c, we can take c out of the equation to get

sin(55°)/8 = sinB/b

If we know sinB, we can multiply both sides by 8 to remove a denominator to get

sin(55°) * b / 8 = sinB

multiply both sides by 8 to remove the other denominator to get

sin(55°) * b = sinB * 8

divide both sides by sin(55°) to isolate the b

b = sinB * 8/sin(55°).

Therefore, if we know sinB, we can figure out the length of b.

Because the angles of a triangle add up to 180 degrees, we can say that

180 = 82 + 55 + angle B

180 = 137 + B

subtract both sides by 137 to isolate B

43 = B

b= sin(43°) * 8 / sin(55°) ≈ 6.7

You might be interested in
A line is drawn so that it passes through the points (-3, -1) and (4, 2).
marishachu [46]

Answer:

(A) \boxed{\bold{y=\frac{3}{7}x+\frac{2}{7}}}

(B) \boxed{\bold{2 \ = \ \frac{3}{7} * \ 4 \ + \ \frac{2}{7}  }}

Explanation:

(A) Slope: y = mx + b

m = 3/7

b = 2/7

Slope = \bold{\frac{y_2-y_1}{x_2-x_1}}

\bold{\left(x_1,\:y_1\right)=\left(-3,\:-1\right),\:\left(x_2,\:y_2\right)=\left(4,\:2\right)}

M = \bold{\frac{2-\left(-1\right)}{4-\left(-3\right)}: \ \frac{3}{7} }

Y intercept

\bold{y=\frac{3}{7}x+b}

Plug in \bold{\left(-3,\:-1\right)\mathrm{:\:}\quad \:x=-3,\:y=-1}

\bold{-1=\frac{3}{7}\left(-3\right)+b}

Isolate B

\bold{-1=\frac{3}{7}\left(-3\right)+b}

b = \bold{\frac{2}{7} }

(B) 4 = x, 2 = y

2 = 3/7 * 4 + 2/7

5 0
3 years ago
Read 2 more answers
What is the solution set of x^2+y^2=26 and x-y=6?
lubasha [3.4K]
I think it's B because it's makes the most sense
5 0
3 years ago
PLEASEEEE HELPPPP ASAP(Essay Worth 10 points)
blagie [28]

Answer:

its worth 5 no 10 :(

Step-by-step explanation:

3 0
3 years ago
Simplify the expression.<br><br> 10 + 3(2v - 3)
Vikentia [17]

Answer:

6v+1

Step-by-step explanation:

7 0
3 years ago
Write an expression that represents the sum of x and 8
krok68 [10]

Answer:

x+8

Step-by-step explanation:

we know that

The phrase " the sum of x and 8" is equivalent to adds the number x and the number 8 or sum the number x plus the number 8

so

x+8

6 0
3 years ago
Other questions:
  • Lucy's car gets 32 miles per gallon of gasoline. How many miles can she drive on 4 gallons of gas?
    8·2 answers
  • 8 times a number is greater than 64
    12·1 answer
  • The following examples illustrate the inverse property of addition. Study the examples, then choose the statement that best desc
    5·1 answer
  • The microwave oven was invented in 1945 when some experiments with radar equipment failed and melted some nearby chocolate inste
    7·2 answers
  • Kena Bought 2 pounds of cheese for 8.00. There are 16 ounces in pound. How much does 16 ounces of cheese cost?
    12·1 answer
  • The Americans with Disabilities Act (ADA) requires a straight ramp have a slope no greater than 1/12.
    6·1 answer
  • Which of the following is a factor of 2x*3 - 2
    11·1 answer
  • If the mean of symmetrical distribution is 28, which of these values could be the median of the distribution.
    15·1 answer
  • Please help me with this homework
    14·2 answers
  • . Write a number in which the value of<br> the 6 is one tenth the value of the 6 ir<br> 35,629.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!