Question

help

Answer 1

A ladder rest against a wall forming 40’ angle with floor. Use the function y=8 sec theta to find the length of the ladder to the nearest foot.

Answer 2

I'm guessing that y is the hypotenuse of the triangle.
8 Feet is opposite of theta but if we are using secant it should be adjacent.

Answer 3

Is there any other information with this problem?

Answer 4

no

Answer 5

Okay well do we agree with my drawing of the problem?

Answer 6

yes

Answer 7

I'm retyping that to make it clearer

****************************************************
Well the COSECANT of 40° = hyp / opp

COSECANT of 40° = hyp / 8

hypotenuse = csc (40°) * 8

Answer 8

hypotenuse = 1.5557 * 8
hypotenuse (or ladder height) = 12.4456

Answer 9

where you get the 1.5557

Answer 10

It is the cosecant of 40°

Answer 11

ok

Answer 12

I see now

Answer 13

so the nearest foot is 12 ft

Answer 14

The answer is okay with you.
As I said I changed the problem. If I worked with secant instead of cosecant, the answer would not be the same.
Secant (40°) = 1.3054

So answer would be 1.3054 * 8

Answer 15

Oh geez - I forgot to round it - yes it rounds to 12
(I guess I felt it was more important to get the problem worded correctly.)

Answer 16

10ft

Answer 17

Why did you round it to 10 feet?
I spent all that time explaining how the problem was worded INCORECTLY.

Answer 18

1.3054*8=10.44

Answer 19

Yes but I added that at the end to say that is the incorrect answer. By the way how familiar are you with trig?

Answer 20

Okay - based on the INCORRECT way the problem is stated then the INCORRECT answer is 10. Maybe everyone else in your class (including the instructor) will say 10.

Answer 21

but the correct is 12 ft

Answer 22

I am just guessing that the problem is worded INCORRECTLY.
I say the problem should be using COSECANT and NOT secant.
The answer should be 12. Show it to your instructor if he says it is wrong.

Suppose (as an example) that a problem says Jack Smith (20 years old) has a SON who is 40 years old , etc
Wouldn't you say there's an error in there?

Answer 23

yes
and just to return to the Jack Smith problem if we answered that Jack Smith (the 20 year old father) has a son who is 40 years old then the son is -20 years (that's MINUS 20 years) younger than the father.
Okay let's head on to the new problem. :-)

Answer 24

If a pebble is dropped into a pond in the shape of an ellipse at the location of one focus, the waves will converge at the location of the other focus. If the pond has a major axis of 20 feet and a minor axis of 12 feet, how far apart are the foci?

Answer 25

Wow - I have a web page that can calculate ellipses.
The foci distance = 16 feet
http://1728.org/ellipse.htm
I can show the math (which you will probably will need right?)

Answer 26

not sure how to input the info

Answer 27

Okay where it says "Which two items of data do you want to input?"
Click on the box "Major Axis and Minor Axis"
Then you'll see the 2 boxes that need to be filled in.
If you need more help, let me know.

Answer 28

but how do you do it manually?

Answer 29

can you use it to find the foci of a hyperbola with an equation?

Answer 30

No - I do not have a hyperbola calculator.

You want the actual ellipse mathematics right?
Are you familiar with the Pythagorean Theorem?

Answer 31

a^2+b^2=c^2

Answer 32

yes !!!!
that is the pyth theorem

Answer 33

yep

Answer 34

okay - geez I have phone call I will return here - about 30 minutes
promise

Answer 35

ok

Answer 36

Link to wikipedia
http://en.wikipedia.org/wiki/Ellipse
Also, look at the diagram at the upper left on this page:
http://1728.org/ellipse.htm
Line Cf1 = half the major axis
Line CO = half the minor axis
Major Axis = 20 feet
Minor Axis = 12 feet
Line Cf1 = 10 feet
Line CO = 6 feet

From Pythagorean Theorem:
Line (f1O)² = (Cf1)² -(CO)²
Line (f1O)² = 10² -6²
Line (f1O)² = 100 -36
Line (f1O)² = 64
Line f1O = 8
Foci distance = Line f1f2 = 2 * 8 =
16

There you go - and yes it is just that "simple" LOL
good luck

Answer 37

Thanks

Answer 38

u r welcome