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
anyanavicka [17]
2 years ago
15

The bearing of Q from P is 150

Mathematics
1 answer:
Lynna [10]2 years ago
8 0

Answer:

(i) see first attached diagram

(ii) QR = 22.67 km (2 dp)

(iii) 243°

Step-by-step explanation:

A bearing is the angle in degrees measured clockwise from north.

<u />

<u>Part (i)</u>

see first attached diagram

<u>Part (ii)</u>

The angles marked in blue on the second attached diagram are Consecutive Interior Angles.  In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°        

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

<u>Part (iii)</u>

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

You might be interested in
Write an algebraic expression for the product of a number squared and 4
S_A_V [24]
Let n represent unknown number
4n^2 is the final answer. Hope it help!
3 0
3 years ago
A rectangle measures 6 3/4 cm by square root of 121 cm. What is the perimeter of the rectangle to the nearest tenth?​
Anni [7]

Answer:

35.5 cm

Step-by-step explanation:

The perimeter (P) is calculated as

P = (2 × 6.75 ) + (2 × \sqrt{121} )

  = 13.5 + (2 × 11) = 13.5 + 22 = 35.5 cm

4 0
3 years ago
Read 2 more answers
Mason and Nora decided to swim across the river. Mason began swimming 3 seconds earlier than Nora.
hram777 [196]
What does 5.3+1 mean
7 0
2 years ago
You bought two tickets to the movies at a price of $7 and six tickets at a price of $5
Stels [109]

Hello! They answer to your question would be that you spent $44. This was because 7*2=14 and 6*5-30. Therefore, 14+30=44.

4 0
3 years ago
855000000000 in scientific notation pls help ASAP!!!
igor_vitrenko [27]

Answer:

8.55 × 10^{11}

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • - 10<br>51<br>76<br>13<br>69<br>79<br>18<br>20<br>2<br>1​
    14·1 answer
  • I dont know the answer to this 29.2 km = _____ dam
    14·2 answers
  • 20x^2 -11x -4 = 0 what are the solutions for this equation
    14·1 answer
  • There are 220 tickets to a school's annual awards banquet. Each adult ticket, a, cost $25 in each student ticket, s, cost $15 ev
    12·1 answer
  • 19 times 8 in expanded form
    13·1 answer
  • Is ABCD a parallelogram?Explain how you know?<br><br> Is EFGH a parallelogram?Explain how you know?
    11·1 answer
  • Question 8 of 10 (1 point)
    11·1 answer
  • Which ordered pair is a solution to the system of inequalities?<br> y&lt; 3x<br> y&lt;5
    8·1 answer
  • Trevor began his pizza delivery route with 7/10 of a tank of gas in his car. When he made it back to the pizzeria, 2/5 of a tank
    15·1 answer
  • a lump sum of $2000 is invested at 4.2% compounded continuously. (a) write the function for the model that gives the future valu
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!