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In triangle ABC, AB = 10cm, BC = 7cm and angle BAC = 40°
(a) Find, in degrees to the nearest 0.1°, the two possible sizes of angle ACB.
(b) Find, in cm to 3 significant figures, the difference between the two possible lengths of AC.
I came across this when looking through the edexcel further pure maths past papers
I got question (a) pretty easily,
i also got question(b) using the cosine rule,and the answer is also correct but
When i read through the mark scheme
the solution given is by drawing a isosceles triangle BCC',
then finding half of the base length CC"=7cos 66.67° and doubling CC'.
How does this method works?I cannot seem to understand it.
Here is the link to the mark scheme.
The question number is 5.
https://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/4PM0_01_rms_20170823.pdf
trigonometry
asked Jul 27 at 15:32
The Black Pyramid
41
add a comment |Â
up vote
0
down vote
favorite
In triangle ABC, AB = 10cm, BC = 7cm and angle BAC = 40°
(a) Find, in degrees to the nearest 0.1°, the two possible sizes of angle ACB.
(b) Find, in cm to 3 significant figures, the difference between the two possible lengths of AC.
I came across this when looking through the edexcel further pure maths past papers
I got question (a) pretty easily,
i also got question(b) using the cosine rule,and the answer is also correct but
When i read through the mark scheme
the solution given is by drawing a isosceles triangle BCC',
then finding half of the base length CC"=7cos 66.67° and doubling CC'.
How does this method works?I cannot seem to understand it.
Here is the link to the mark scheme.
The question number is 5.
https://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/4PM0_01_rms_20170823.pdf
trigonometry
asked Jul 27 at 15:32
The Black Pyramid
41
To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
In triangle ABC, AB = 10cm, BC = 7cm and angle BAC = 40°
(a) Find, in degrees to the nearest 0.1°, the two possible sizes of angle ACB.
(b) Find, in cm to 3 significant figures, the difference between the two possible lengths of AC.
I came across this when looking through the edexcel further pure maths past papers
I got question (a) pretty easily,
i also got question(b) using the cosine rule,and the answer is also correct but
When i read through the mark scheme
the solution given is by drawing a isosceles triangle BCC',
then finding half of the base length CC"=7cos 66.67° and doubling CC'.
How does this method works?I cannot seem to understand it.
Here is the link to the mark scheme.
The question number is 5.
https://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/4PM0_01_rms_20170823.pdf
trigonometry
asked Jul 27 at 15:32
The Black Pyramid
41
In triangle ABC, AB = 10cm, BC = 7cm and angle BAC = 40°
(a) Find, in degrees to the nearest 0.1°, the two possible sizes of angle ACB.
(b) Find, in cm to 3 significant figures, the difference between the two possible lengths of AC.
I came across this when looking through the edexcel further pure maths past papers
I got question (a) pretty easily,
i also got question(b) using the cosine rule,and the answer is also correct but
When i read through the mark scheme
the solution given is by drawing a isosceles triangle BCC',
then finding half of the base length CC"=7cos 66.67° and doubling CC'.
How does this method works?I cannot seem to understand it.
Here is the link to the mark scheme.
The question number is 5.
https://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/4PM0_01_rms_20170823.pdf
trigonometry
asked Jul 27 at 15:32
The Black Pyramid
41
edited Jul 27 at 15:46
asked Jul 27 at 15:32
The Black Pyramid
41
asked Jul 27 at 15:32
The Black Pyramid
41
asked Jul 27 at 15:32
The Black Pyramid
41
41
To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18
add a comment |Â
To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18
To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18
add a comment |Â
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To find location of point $C$ first construct $AB$ and then angle $BAC$. There will be two ways to construct the angle. Then draw a height from $BC$, this will give you two right triangles and you can find all angles and sides.
– Vasya
Jul 27 at 15:41
Draw in their figure from 5(b) the point C'' as the mid point of the base CC' of the isosceles triangle BCC' with BC = BC' = 7. We know from the previous point the angle in C', then consider the triangle BCC", using the cos of <)C' get first C'C", then double it to get CC', the wanted difference.
– dan_fulea
Jul 27 at 15:51
The given data (Side-Side-Angle) is not enough to determine a Congruence of triangles. In this case two separate triangles can be constructed, that is The ambiguous case of triangle solution
– Jon
Jul 27 at 16:15
Thanks for the explanation ,guys
– The Black Pyramid
Jul 27 at 16:18