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
natka813 [3]
3 years ago
13

Group A is on the north side of the fire and is 800 ft away from group B and 900 feet away from group C. Group A knows that the

angle between its two adjacent sides is 89.6. “
The emergency responders want to properly inform the nearby towns of the danger proximity. They will need all three angles. To do this they need some additional information. The emergency responders need to know the angle of Group B and Group C. They also need to know the distance between Groups B and C.

Mathematics
1 answer:
hram777 [196]3 years ago
4 0

Answer:

1. Length BC is 1200 ft

2. Angle B is 48.6°

3. Angle C is 41.8°

Step-by-step explanation:

1. Determination of the length BC

Side opposite C = c = 800 ft

Side opposite B = b = 900 ft

Angle A = 89.6°

Side opposite BC = a =?

Using cosine rule, we can obtain length BC as follow:

a² = b² + c² – 2bc CosA

a² = 900² + 800² – 2 × 900 × 800 × Cos89.6

a² = 810000 + 640000 – 1440000 × 0.007

a² = 1450000 – 10080

a² = 1439920

Take the square root of both side

a = √1439920

a ≈ 1200 ft

Thus, length BC is 1200 ft

2. Determination of angle B

Side opposite B = b = 900 ft

Side opposite A = a = 1200 ft

Angle A = 89.6°

Angle B =?

Angle B can be obtained by using sine rule as follow:

a / Sine A = b / Sine B

1200 / Sine 89.6° = 900 / Sine B

Cross multiply

1200 × Sine B = 900 × Sine 89.6°

1200 × Sine B = 900

Divide both side by 1200

Sine B = 900/1200

Sine B = 0.75

Take the inverse of Sine

B = Sine¯¹ 0.75

B = 48.6°

Thus, angle B is 48.6°

3. Determination of angle C

Side opposite C = c = 800 ft

Side opposite A = a = 1200 ft

Angle A = 89.6°

Angle C =?

Angle C can be obtained by using sine rule as follow:

a / Sine A = c / Sine C

1200 / Sine 89.6° = 800 / Sine B

Cross multiply

1200 × Sine C = 800 × Sine 89.6°

1200 × Sine C = 800

Divide both side by 1200

Sine C = 800/1200

Sine C = 0.6667

Take the inverse of Sine

C = Sine¯¹ 0.6667

C = 48.6°

Thus, angle C is 41.8°

You might be interested in
Write 187.023 in word form
riadik2000 [5.3K]
One hundred eighty-seven and twenty-three thousandths
<span />
4 0
3 years ago
Read 2 more answers
Write the slope-intercept form of the equation of the line that is perpendicular to AB and passes through Point X. Show all work
aleksandr82 [10.1K]

Answer:

Equation of line is y=(12/5)x+2

Step-by-step explanation:

The slope of line AB is -5/12. The line passing X is perpendicular to line AB and hence have a slope of 12/5. The slope intercept form is given by y=mx+c.

Now, point X satisfies the equation. Plugging in the slope of the line we end up with

y=(12/5)*x+c, now to find c

-10=(12/5)*(-5)+c, c=2

Equation of line is y=(12/5)x+2

7 0
3 years ago
Compare the functions.
marshall27 [118]

Function h has the largest y-intercept which is 44

Step-by-step explanation:

Any linear function is represented in the form

f(x) = mx+b

Here b is the y-intercept of the linear function i.e. the constant term in the function.

We will compare all the functions with the general form we get

y-intercept of f(x) = 1

y-intercept of g(x) = 8

y-intercept of h(x) = 44

y-intercept of j(x) = 0

Hence,

Function h has the largest y-intercept which is 44

Keywords: intercepts, linear functions

Learn more about intercepts at:

  • brainly.com/question/9532142
  • brainly.com/question/9590016

#LearnwithBrainly

5 0
3 years ago
Solve the system by elimination<br><br> 2 + 5 = −24<br> 3 − 5 = 14
belka [17]

Answer:

7=24

-2 = 14

Step-by-step explanation:

(2+5)= 7=24

8 0
3 years ago
❗️❗️PLEASE HELP ME❗️❗️
kicyunya [14]

question 3 = $150 because 50% is one half of 100% so 300/2 = 150

4 0
2 years ago
Read 2 more answers
Other questions:
  • This is a math problem, how do I round 0.975 to the nearest tenth
    12·2 answers
  • FInd the equation of a perpendicular line to y=-2 that passes through the points (4,-2)
    10·1 answer
  • Which equations are equivalent? Select all that apply. 1 + x = 3 x – 4 = -2 1 + x = -2 x + 3 = 5 x – 5 = 3
    5·2 answers
  • Which of the following has a slope of -3 and a y-intercept of -4 ?
    5·1 answer
  • Geometry help, will upvote best answer!!
    9·2 answers
  • What expression can be used to convert 80 US dollars to australian dollars
    12·1 answer
  • Car A travels at an average speed of 45 miles per hour. Car B travels at an average speed of 40 miles per hour. In the time it t
    12·1 answer
  • Describe the difference between a bar graph and a circle graph.
    6·1 answer
  • In a sale the price of a sofa is reduced by 70%. The price is £255 Work out the price before the sale
    14·1 answer
  • What is the value of a in the equation 304 b =54, when b =9? O 15 O 18 0 21 O 27
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!