Triangle ABE is isosceles / Given
AB congruent to AE / Def isosceles
angle ABE congruent to angle AEB / Property of isosceles triangles
angle ABD congruent to angle AEC / Subst different name for same angles
BD congruent to EC / Given
triange ABD congruent to triange AEC / Side Angle Side
First one:
cos(A)=AC/AB=3/4.24
cos(B)=BC/AB=3/4.24
Cos(A)/cos(B)=AC/AB / (BC/AB) = AC/AB * AB/BC = AC/BC=3/3=1
Second one:
To solve this problem, we have to ASSUME AFE is a straight line, i.e. angle EFB is 90 degrees. (this is not explicitly given).
If that's the case, AE is a transversal of parallel lines AB and DE.
And Angle A is congruent to angle E (alternate interior angles).
Therefore sin(A)=sin(E)=0.5
The charge on each house is 8 units
Slope=rise/run
yintercept is where the line crosses the y axis
y=mx+B
m=slope
b=yint
intercept at -3
y=mx-3
pick a point
(5,0)
x=5,y=0
0=m(5)-3
add 3
3=5m
divide 5
3/5=m
slope=3/5
y int=-3
