Question

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:


A scientist measures the angle x and the distance y between the Sun and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the moon.

Answer 1

plz help!!!!!

Answer 2

@campbell_st
@ganeshie8
@mathstudent55
@phi

Answer 3

plz help!!!

Answer 4

its because a 3rd measurement is given... its the right angle...

and using right angled trigonometry you can find the distance between the earth and the moon.

Answer 5

what is the third measurement

Answer 6

?

Answer 7

the right angle..... its given to you in the diagram

Answer 8

I'm confused on what to do

Answer 9

can u help me to understand?

Answer 10

ok... so this is a question about trigonometry

in angle right triangle.... of you are given

1 angle and 1 side measure, you can find another side measure using trigonometry

the distance from the earth to the moon is opposite the angle x

you have a measure for the hypotenuse.... y

so using the sin ratio sin(x) = opp/hyp

you can find the distance

it would be sin(x) = (Earth to moon)/y

so manipulating the equation

Earth to Moon = y * sin(x)

Answer 11

but there aren't any numbers for the equation @campbell_st

Answer 12

do i do it with the variables?

Answer 13

that's correct.... the questioner is asking in general terms.... how can you use the 2 given measures to find a 3rd....

so the value of x could be 12 degrees and y = 1000000 km....

or you could select any pair you like... but 12 and 1000000 is a specific case

Answer 14

i have no idea what to do @campbell_st

Answer 15

how can i use that for my question?

Answer 16

@radar

Answer 17

@tHe_FiZiCx99

Answer 18

say the scientist is cheating as there is a 3rd measure given, the right angle.

Knowing that a right angle has been formed the scientist will is trigonometry, specifically the sin ratio to find the distance from the earth to the moon.

if the distance from the earth to the moon is d then

\[\sin(x) = \frac{d}{y}\]

which becomes \[d = y \times \sin(x)\]

and this is another classic example as to why math come before science.

hope it helps

Answer 19

but how the scientist can use only these two measurements to calculate the distance between the Earth and the moon? @campbell_st

Answer 20

what r the measurements?
the variables?

Answer 21

the equation above only uses 2 measures... x and y

Answer 22

there are variables... which means the vary.... x could be any angle less than 90

Answer 23

but how can we use them when we don't have any numbers

Answer 24

the equation above says to find d, you only need x and y

Answer 25

perhaps you should ask your teacher to explain variables.....

Answer 26

how do i find what they are?

Answer 27

not they have to have values?

Answer 28

dont

Answer 29

you don't need to know.... you are being asked to provide a general solution... which covers all cases for x and y

Answer 30

ok can u help me answer my question?

Answer 31

sorry... I have to go to school.

Answer 32

from who can i get help from?

Answer 33

just post the question... and someone will look at it

Answer 34

how much time do u have before getting off the computer?

Answer 35

@phi

Answer 36

@mathstudent55

Answer 37

@mathstudent55

Answer 38

plz help!

Answer 39

The Earth_Moon distance is equal to the product of the Moon_Sun distance, y, and the Sine of angle x.

Answer 40

ok but how do i do this?

Answer 41

what am i supposed to do

Answer 42

i don't have numbers

Answer 43

i wrote that they can use them to find the third measurement
how do i add more to that?

Answer 44

In the problem statement, the scientist has measured y and angle x.
The measurement numbers are not given and we do not have access to his notes.

The statement:

The Earth_Moon distance is equal to the product of the Moon_Sun distance, y, and the Sine of angle x.

is in effect a formula, a method, directions, process, to calculate the Earth_Moon distance.

Answer 45

ok so we can use them for the third measurement?

Answer 46

Yes.

Answer 47

wait this is what i wrote

Answer 48

you can use the trigonometric functions and angle x and distance y to get the third measurements. we can use angle x and distance y to find out what the earth to moon distance is

Answer 49

what else should i add

Answer 50

You might put in the an actual trig function such as:

ie. the earth to moon distance is equal to y sin(x).

Answer 51

anything else?

Answer 52

just add that in?

Answer 53

I cannot guarantee what your instructor will say, but it sounds like you now have the central idea.

Answer 54

can u help me with another one?

An observer (O) is located 900 feet from a building (B). The observer notices a helicopter (H) flying at a 49° angle of elevation from his line of sight. How high is the helicopter flying over the building? You must show all work and calculations to receive full credit.

Answer 55

With this type of trig problem divide the unknown, h, by 900 and then ask yourself what trig function does this ratio represent. Tangent for this problem.
Now h/900 = Tan(49) or h = 900 Tan(49.)
This is how I worked out the astronomy problem.

Answer 56

i got 1035.3315665

Answer 57

is it right

Answer 58

Yes. And to wow your class mates as such, here it is to 20 decimal digtis from Mathematic 9 Home Edition.
1035.3315664989086003

Answer 59

yay!!!!!!!

Answer 60

and can u check a problem

Explain the difference between using the tangent ratio to solve for a missing angle in a right triangle versus using the cotangent ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view.

i put
the answers come out to be reciprocals. except that there is no other difference.

Answer 61

is it good enough? what else should i add?

Answer 62

I think that I would leave it as one is the reciprocal of the other.
Strictly speaking, each has specific coressponding side ratios.
One could have invented the Tangent and not given the Cotangent a name.

Answer 63

???

Answer 64

so just say that they are reciprocals?

Answer 65

Yes.
Are you being tought from a "Common Core" text book?

Answer 66

i dont know

Answer 67

thank u very much!!!!

Answer 68

Your are welcome.