Answer:
Step-by-step explanation:
a) Yes.
b) Yes
c) Yes
d) No
Answer:
the answer is D 1/27
Step-by-step explanation:
Answer:
y=6
Step-by-step explanation:
I'll talk you through it so you can see why it's true, and then
you can set up the 2-column proof on your own:
Look at the two pointy triangles, hanging down like moth-wings
on each side of 'OC'.
-- Their long sides are equal, OA = OB, because both of those lines
are radii of the big circle.
-- Their short sides are equal, OC = OC, because they're both the same line.
-- The angle between their long side and short side ... the two angles up at 'O',
are equal, because OC is the bisector of the whole angle there.
-- So now you have what I think you call 'SAS' ... two sides and the included angle of one triangle equal to two sides and the included angle of another triangle.
(When I was in high school geometry, this was not called 'SAS' ... the alphabet
did not extend as far as 'S' yet, and we had to call this congruence theorem
"broken arrow".)
These triangles are not congruent the way they are now, because one is
the mirror image of the other one. But if you folded the paper along 'OC',
or if you cut one triangle out and turn it over, it would exactly lie on top of
the other one, and they would be congruent.
So their angles at 'A' and at 'B' are also equal ... those are the angles that
you need to prove equal.
The two planes are flying on the two legs of a right triangle.
The straight distance between them is the hypotenuse of the triangle.
Since the speeds are in mph, let's work the time in hours.
Call the time 'H' that we're looking for.
It's the number of hours after they both take off that they're 650 miles apart.
After 'H' hours, the first plane has gone 500H miles north.
After 'H' hours, the second plane has gone 1200H miles east.
After 'H' hours, they are 650 miles apart.
Do you remember this for a right triangle ? ==> A² + B² = C²
(500H)² + (1200H)² = (650)²
250,000H² + 1,440,000H² = 422,500
1,690,000 H² = 422,500
H² = (422,500) / (1,690,000) = 0.25
H = √0.25 = 1/2 hour = 30 minutes
