Working with Radial Surveys 2
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Question 1 of 4
1. Question
From the radial survey below, find the following:
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`(i) angleBOC=` (74)`°``(ii) angleBOA=` (128)`°`
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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)` `angleBOC`Notice that `angleBOC` is the difference between the bearings of `B` and `C`.Subtract the bearing of `B` from the bearing of `C`.`angleBOC` `=` `angleC-angleB` `=` `139°-65°` Substitute the values `=` `74°` 
`(ii)` `angleBOA`Notice that `angleBOA` is the sum of the bearing of `B` and `angleNOA`.Add the bearing of `B` to `angleNOA`.`angleBOA` `=` `angleNOA+angleB` `=` `63°+65°` Substitute the values `=` `128°` 
`(i)/_BOC=74°``(ii)/_BOA=128°` -
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Question 2 of 4
2. Question
From the radial survey below, find the length of `BC`.
Round your answer to `2` decimal places- `BC=` (60.83)`m`
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Cosine Law
$$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$where:
`a` is the side opposite angle `A`
`b` is the side opposite angle `B`
`c` is the side opposite angle `C`Since `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 `BC` or `a`.From labelling the triangle, we know that the known values are those with labels `A, b` and `c`.`A=74°``b=49m``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` `=` `5105-5096cos74°` Evaluate `cos` `74` on your calculator `a^2` `=` `5105-5096(0.275637)` `a^2` `=` `5105-1404.64797` `a^2` `=` `3700.35203` `sqrt(a^2)` `=` `sqrt3700.35203` Take the square root of both sides `a` `=` `60.8305m` `a` or `BC` `=` `60.83m` Round off to `2` decimal places 
`60.83m` -
Question 3 of 4
3. Question
From the radial survey below, find the length of `BA`.
Round your answer to `2` decimal places- `BA=` (92.58)`m`
Hint
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Cosine Law
$$\color{#007DDC}{a}^2=\color{#00880A}{b}^2+\color{#9a00c7}{c}^2-2\color{#00880A}{b}\color{#9a00c7}{c}\cos\color{#007DDC}{A}$$where:
`a` is the side opposite angle `A`
`b` is the side opposite angle `B`
`c` is the side opposite angle `C`Since `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 `BA` or `c`.From labelling the triangle, we know that the known values are those with labels `C, a` and `b`.`C=128°``b=51m``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` `=` `5305-5304cos128°` Evaluate `cos` `128` on your calculator `c^2` `=` `5305-5304(-0.615661475)` `c^2` `=` `5305+3265.4685` `c^2` `=` `8570.4685` `sqrt(c^2)` `=` `sqrt8570.4685` Take the square root of both sides `c` `=` `92.5768m` `c` or `BA` `=` `92.58m` Round off to `2` decimal places 
`92.58m` -
Question 4 of 4
4. Question
Find the perimeter of the field shown by this radial survey.
- (253.41)`m`
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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.
`AO=51m``OC=49m``BC=60.83m``BA=92.58m`Perimeter `=` `AO+OC+BC+BA` `=` `51+49+60.83+92.58` Substitute the values `=` `253.41m` `253.41m`