You said X = (5y+1) / (y-2)
Multiply each side by (y-2):
X(y-2) = (5y+1)
Eliminate parentheses:
Xy - 2X = 5y + 1
Add 2X to each side:
Xy = 5y + 1 + 2X
Subtract 5y from each side:
(X-5)y = 1 + 2X
Divide each side by (X-5):
<em>y = (1+2X) / (X-5) </em>
I use the sin rule to find the area
A=(1/2)a*b*sin(∡ab)
1) A=(1/2)*(AB)*(BC)*sin(∡B)
sin(∡B)=[2*A]/[(AB)*(BC)]
we know that
A=5√3
BC=4
AB=5
then
sin(∡B)=[2*5√3]/[(5)*(4)]=10√3/20=√3/2
(∡B)=arc sin (√3/2)= 60°
now i use the the Law of Cosines
c2 = a2 + b2 − 2ab cos(C)
AC²=AB²+BC²-2AB*BC*cos (∡B)
AC²=5²+4²-2*(5)*(4)*cos (60)----------- > 25+16-40*(1/2)=21
AC=√21= 4.58 cms
the answer part 1) is 4.58 cms
2) we know that
a/sinA=b/sin B=c/sinC
and
∡K=α
∡M=β
ME=b
then
b/sin(α)=KE/sin(β)=KM/sin(180-(α+β))
KE=b*sin(β)/sin(α)
A=(1/2)*(ME)*(KE)*sin(180-(α+β))
sin(180-(α+β))=sin(α+β)
A=(1/2)*(b)*(b*sin(β)/sin(α))*sin(α+β)=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
KE/sin(β)=KM/sin(180-(α+β))
KM=(KE/sin(β))*sin(180-(α+β))--------- > KM=(KE/sin(β))*sin(α+β)
the answers part 2) areside KE=b*sin(β)/sin(α)side KM=(KE/sin(β))*sin(α+β)Area A=[(1/2)*b²*sin(β)/sin(α)]*sin(α+β)
Don't get too involved in the 'simplify' part just yet.
It doesn't mean make the problem easier.
It means that when you have the answer, make sure it's in simplest form.
That's why it says "Simplify your answer".
Notice that that's the 2nd instruction.
There's nothing to simplify until you have an answer.
The first thing you have to do here is find the area of a triangle.
Do you remember that formula ?
I'll bet you do.
The area of a triangle is (1/2) · (length of the base) · (height) .
The height and the length of the base are given, right there
in the picture. Take those, and use them to find the area.
Once you've multiplied the binomials, don't forget about the (1/2).
Finally, you have a trinomial for an answer.
Put the big sweet cherry on top: Factor it !
I think that's the 'simplify' part.
You may be surprised.
I was when I worked it out just now ... just for you.
