Working with Radial Surveys 2

Years

Year 12

Bearings

Working with Radial Surveys

Working with Radial Surveys 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 4

1. Question
From the radial survey below, find the following:
- $(i) ∠ B O C =$ $(i) angleBOC=$ (74) $°$ $°$
  
  $(i i) ∠ B O A =$ $(ii) angleBOA=$ (128) $°$ $°$
Hint

Help Video
Correct

Fantastic!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

A radial survey is a tool used for land and seafloor mapping. Each corner of the area being measured is connected to a central point.

$(i)$ $(i)$ $∠ B O C$ $angleBOC$

Notice that $∠ B O C$ $angleBOC$ is the difference between the bearings of $B$ $B$ and $C$ $C$ .

Subtract the bearing of $B$ $B$ from the bearing of $C$ $C$ .

$∠ B O C$ $angleBOC$ $=$ $=$ $∠ C - ∠ B$ $angleC-angleB$

$=$ $=$ $139 ° - 65 °$ $139°-65°$ Substitute the values

$=$ $=$ $74 °$ $74°$

$(i i)$ $(ii)$ $∠ B O A$ $angleBOA$

Notice that $∠ B O A$ $angleBOA$ is the sum of the bearing of $B$ $B$ and $∠ N O A$ $angleNOA$ .

Add the bearing of $B$ $B$ to $∠ N O A$ $angleNOA$ .

$∠ B O A$ $angleBOA$ $=$ $=$ $∠ N O A + ∠ B$ $angleNOA+angleB$

$=$ $=$ $63 ° + 65 °$ $63°+65°$ Substitute the values

$=$ $=$ $128 °$ $128°$

$(i) ∠ B O C = 74 °$ $(i)/_BOC=74°$

$(i i) ∠ B O A = 128 °$ $(ii)/_BOA=128°$

Question 2 of 4

From the radial survey below, find the length of

B C

$BC$ .

Round your answer to

2

$2$ decimal places

$B C =$ $BC=$ (60.83) $m$ $m$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Cosine Law

a^{2} = b^{2} + c^{2} - 2 b c \cos A

$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$

where:
$a$ $a$ is the side opposite angle $A$ $A$
$b$ $b$ is the side opposite angle $B$ $B$
$c$ $c$ is the side opposite angle $C$ $C$

Since

2

$2$ sides are given together with an angle between them, use the Cosine Law.

First, label the triangle according to the Cosine Law.

Substitute the three known values to the Cosine Law to find the length of side

B C

$BC$ or $a$ $a$ .

From labelling the triangle, we know that the known values are those with labels

A, b

$A, b$ and

c

$c$ .

A = 74 °

$A=74°$

b = 49 m

$b=49m$

c = 52 m

$c=52m$

$\color{#007DDC}{a}^2$	$=$ $=$	$\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$
$\color{#007DDC}{a}^2$	$=$ $=$	$\color{#00880A}{49}^2+\color{#9a00c7}{52}^2-2(\color{#00880A}{49})(\color{#9a00c7}{52})\cos\color{#007DDC}{74°}$	Substitute the values
$a^{2}$ $a^2$	$=$ $=$	$5105 - 5096 \cos 74 °$ $5105-5096cos74°$	Evaluate $\cos$ $cos$ $74$ $74$ on your calculator
$a^{2}$ $a^2$	$=$ $=$	$5105 - 5096 (0.275637)$ $5105-5096(0.275637)$
$a^{2}$ $a^2$	$=$ $=$	$5105 - 1404.64797$ $5105-1404.64797$
$a^{2}$ $a^2$	$=$ $=$	$3700.35203$ $3700.35203$
$\sqrt{a^{2}}$ $sqrt(a^2)$	$=$ $=$	$\sqrt{3700.35203}$ $sqrt3700.35203$	Take the square root of both sides
$a$ $a$	$=$ $=$	$60.8305 m$ $60.8305m$
$a$ $a$ or $B C$ $BC$	$=$ $=$	$60.83 m$ $60.83m$	Round off to $2$ $2$ decimal places

60.83 m

$60.83m$

Question 3 of 4

From the radial survey below, find the length of

B A

$BA$ .

Round your answer to

2

$2$ decimal places

$B A =$ $BA=$ (92.58) $m$ $m$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Cosine Law

a^{2} = b^{2} + c^{2} - 2 b c \cos A

$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$

where:
$a$ $a$ is the side opposite angle $A$ $A$
$b$ $b$ is the side opposite angle $B$ $B$
$c$ $c$ is the side opposite angle $C$ $C$

Since

2

$2$ sides are given together with an angle between them, use the Cosine Law.

First, label the triangle according to the Cosine Law.

Substitute the three known values to the Cosine Law to find the length of side

B A

$BA$ or $c$ $c$ .

From labelling the triangle, we know that the known values are those with labels

C, a

$C, a$ and

b

$b$ .

C = 128 °

$C=128°$

b = 51 m

$b=51m$

a = 52 m

$a=52m$

$\color{#007DDC}{a}^2$	$=$ $=$	$\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$
$\color{#9a00c7}{c}^2$	$=$ $=$	$\color{#00880A}{b}^2+\color{#007DDC}{a}^2-2\color{#00880A}{b}\color{#007DDC}{a}\cos\color{#9a00c7}{C}$	Rewrite the formula according to the given values
$\color{#9a00c7}{c}^2$	$=$ $=$	$\color{#00880A}{51}^2+\color{#007DDC}{52}^2-2(\color{#00880A}{51})(\color{#007DDC}{52})\cos\color{#9a00c7}{128°}$	Substitute the values
$c^{2}$ $c^2$	$=$ $=$	$5305 - 5304 \cos 128 °$ $5305-5304cos128°$	Evaluate $\cos$ $cos$ $128$ $128$ on your calculator
$c^{2}$ $c^2$	$=$ $=$	$5305 - 5304 (- 0.615661475)$ $5305-5304(-0.615661475)$
$c^{2}$ $c^2$	$=$ $=$	$5305 + 3265.4685$ $5305+3265.4685$
$c^{2}$ $c^2$	$=$ $=$	$8570.4685$ $8570.4685$
$\sqrt{c^{2}}$ $sqrt(c^2)$	$=$ $=$	$\sqrt{8570.4685}$ $sqrt8570.4685$	Take the square root of both sides
$c$ $c$	$=$ $=$	$92.5768 m$ $92.5768m$
$c$ $c$ or $B A$ $BA$	$=$ $=$	$92.58 m$ $92.58m$	Round off to $2$ $2$ decimal places

92.58 m

$92.58m$

Question 4 of 4

4. Question
Find the perimeter of the field shown by this radial survey.
- (253.41) $m$ $m$
Hint

Help Video
Correct

Correct!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

A radial survey is a tool used for land and seafloor mapping. Each corner of the area being measured is connected to a central point.

To find the perimeter of the field, simply add the lengths of the sides of the field.

$A O = 51 m$ $AO=51m$

$O C = 49 m$ $OC=49m$

$B C = 60.83 m$ $BC=60.83m$

$B A = 92.58 m$ $BA=92.58m$

Perimeter $=$ $=$ $A O + O C + B C + B A$ $AO+OC+BC+BA$

$=$ $=$ $51 + 49 + 60.83 + 92.58$ $51+49+60.83+92.58$ Substitute the values

$=$ $=$ $253.41 m$ $253.41m$

$253.41 m$ $253.41m$

Working with Radial Surveys 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

2. Question

Hint

Well Done!

Cosine Law

3. Question

Hint

Excellent!

Cosine Law

4. Question

Hint

Correct!

Quizzes

$∠ B O C$ $angleBOC$	$=$ $=$	$∠ C - ∠ B$ $angleC-angleB$
	$=$ $=$	$139 ° - 65 °$ $139°-65°$	Substitute the values
	$=$ $=$	$74 °$ $74°$

$∠ B O A$ $angleBOA$	$=$ $=$	$∠ N O A + ∠ B$ $angleNOA+angleB$
	$=$ $=$	$63 ° + 65 °$ $63°+65°$	Substitute the values
	$=$ $=$	$128 °$ $128°$

Perimeter	$=$ $=$	$A O + O C + B C + B A$ $AO+OC+BC+BA$
	$=$ $=$	$51 + 49 + 60.83 + 92.58$ $51+49+60.83+92.58$	Substitute the values
	$=$ $=$	$253.41 m$ $253.41m$