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
Rina8888 [55]
2 years ago
15

Find each measure measurement indicated. Round your answers to the nearest tenth. Please show work​

Mathematics
2 answers:
miskamm [114]2 years ago
6 0

9514 1404 393

Answer:

  1. ∠B = 125°
  2. ∠y = 27°
  3. DF = 6 km
  4. AC = 12 ft

Step-by-step explanation:

1. The desired angle is given on the diagram as 125°.

__

For the rest of these problems, the Law of Sines applies. A side can be found from ...

  a = b(sin(A)/sin(B))

and an angle can be found from ...

  A = arcsin(a/b·sin(B))

__

2. Y = arcsin(y/z·sin(Z)) = arcsin(5/11·sin(88°))

  ∠Y = 27°

__

3. DF = (11 km)·sin(32°)/sin(103°)

  DF = 5.98 km ≈ 6 km

__

4. b = c·sin(B)/sin(C) = (13 ft)·sin(65°)/sin(180° -65° -37°)

  b = 12 ft

MakcuM [25]2 years ago
5 0

Answer:

#1: The measure of m<B is 125°.

#2: M<Y is equal a 27°.

#3: So the length of DF is 5.99 km.

#4: the side length AC is 13.1 feet.

Explanation:

# 1: The following given,

c = AB = 17 cm

a = BC = unknown

b = CA = 44 cm

Ø = 125

M<B means it is the angle at vertex B of the triangle, it is also the only angle given in thbe figure.

Therefore, The measure of m<B is 125°.

#2: We can calculate the value of the angles by means of the law of sine which is the following:

\frac{yz}{sin \: x}  =  \frac{xz}{sin \: y}  =  \frac{xy}{sin \: z}

We need you know the Y value, therefore we replace and solve for Y

\frac{xz}{sin \: y}  =  \frac{xy}{sin \: z}  \\  \frac{5}{sin \: y}  =  \frac{11}{sin \: 88}  \\ 5 \: . \: sin \: 88 = 11 \: . \: sin \: y \\ sin \: y =  \frac{5 \: . \: sin \: 88}{11} \\ sin \: y = 0.45426 \\ y =  {sin}^{ - 1} (0.45426) \\ y = 27

#3: In order to find the length of Df, we can use the law of sines in this triangle:

\frac{11}{sin \: (103)}  =  \frac{df}{sin \: (32)}  \\  \frac{11}{0.974}  =  \frac{df}{0.53}  \\ df =  \frac{11.0.53}{0.974}  \\ df = 5.99

So the length of DF is 5.99 km.

#4: We are given two two angles and one side length.

<A = 37°

<B = 65°

AB = 13 ft

We are asked to find side length AC

We can use the "law of sines" to find the side length AC

\frac{sin \: c}{ab}  =  \frac{sin \: b}{ac}

Let us first find the angle <C

Recall that the sum of all three interior angles of a triangle must be equal to 180°

< a +  < b +  < c = 180 \\ 37 + 65 +  < c = 180 \\ 102 +  < c = 180 \\  < c = 180 - 102 \\  < c = 78

So, the angle <C is 78°

Now let us substitute all the known values into the law of sines formula and solve for AC

\frac{sin \: c}{ab} =  \frac{sin \: b}{ac}  \\  \frac{sin \: 75}{13}  =  \frac{sin \: 65}{ac}  \\ ac =  \frac{sin \: 65 \: . \: 13}{sin \: 75} \\ ac =  \frac{9.06 \: . \: 13}{0.899}   \\ ac = 13.1ft

Therefore, the side length AC is 13.1 feet.

You might be interested in
Convert the quadratic function from vertex form to standard form: g(x)= 1/2 (x+2)^2-8
Yuri [45]

Answer:

y = 1/2x² - 2x - 6

4 0
1 year ago
Simply (3/10) (-5/9)
frutty [35]

Answer:

-1/10

Step-by-step explanation:

3 x (-5)

-15

10 x (-9)

-90

-15/90 divided by 5

-3/30 divided by 3

-1/10

6 0
3 years ago
How can you find unknown lengths or widths in an easy way?<br> 30 points!
Nadusha1986 [10]
Since you are in middle school, I will assume simple shapes such as rectangles and squares

area=legnth times width
therefor
width=area/legnth and
legnth=area/width
7 0
2 years ago
Help please please help help me!!!!
Flura [38]

Answer:

I got 126.12 in my notes

Step-by-step explanation:

4 0
2 years ago
Help guys don't answer if you don't know​
borishaifa [10]

Answer:

1) Appliances are connected in parallel

2) Appliances are connected in parallel

3) Appliances are connected in parallel (because in house , appliances are connected in parallel)

4) Advantage :- Such kind of connections assures that even if one or more appliances stops working , the working of other appliances will remain unaffected because in such connections , voltage remains constant

Disadvantage :- Such circuits can draw more power which leads to high bill charges on electricity. Also such connections need more wiring.

7 0
3 years ago
Other questions:
  • Drag the similar figure into the table
    7·1 answer
  • A clothing store is raising the price of all its sweaters by $3.00. Write an expression that could be used to find the new price
    9·2 answers
  • An author receives $0.60 for each hardcover book or paperback book that is sold. There were x hardcover books and 38,000 paperba
    13·1 answer
  • Which two numbers have an absolute value of 50
    11·1 answer
  • A bookcase contains 2 statistics books and 5 biology books. if 2 books are chosen at random, the chance that both are statistics
    7·1 answer
  • I have to find the value of X, it’s in spanish:), and im trying to help a friend:)
    9·1 answer
  • What are the x- and y- intercepts for the graph of 5x-2y= 20
    10·1 answer
  • What is the answer of this question I need to know now
    14·1 answer
  • Can y'all help me with my math problem please
    6·1 answer
  • 3.99 million - 47,000,000
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!