Answer:
Question 1:
Find Bc.
make use of SOHCAHTOA.
this means
BC is your A --- adjacent
AB is your O --- opposite
AC is your H --- hypotenuse
since AC is given as well as an angle
AC is H and we need BC which is A .
from the word SOHCAHTOA ... the part which makes use of A and H
is CAH. this means cos
cos 42 = A/H
cos 42 = A/8.1
A = 8.1 cos 4.2
A = 6.4
hence the length of BC is 6.4 cm
Question 3
recognise that DEF is a straight line hence to get BEF
BEF = 180 - 124
angle BEF = 56 degrees
the two small lines on EB and EF , this shows its an isoceles triangle
therefore : angle EFB and angle EBF is the SAME
there fore to get this answer is :
EFB = (180 - BEF )/2
= ( 180 - 56)/2
= 62 degrees
since CBFE is a Z angle ( corresponding angles )
this means
angle EFB =angle FBC
therefore
x = 62 degrees
Question 4
3x + 2y = 1
2x + 3y = 9
we can make use of the elimination method
we have to make the x values the same :
we can multiply one equation by 3 and the other by 2 , this will give the same x values
2(3x + 2y = 1)
= 6x + 4y = 2
3 (2x + 3y = 9)
= 6x + 9y = 27
now we can solve with the new equations:
6x + 4y = 2
6x + 9y = 27
the 6x is crossed out
4y - 9y = 2-27
-5y = -25
y = -25/-5
y = 5
place the value of y into the original equation.
3x + 2y = 1
3x + 2(5) = 1
3x + 10 = 1
3x = 1-10
3x = -9
x = -9/3
x = -3
the values are y = 5 and x = -3
