An airplane is flying at an altitude of 4,600 ft. The pilot sights an object on the ground at an angle of depression of 35°. What is the slant distance from the airplane to the object ?

- anonymous

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- jim_thompson5910

|dw:1441671957196:dw|

- jim_thompson5910

|dw:1441671998905:dw|

- jim_thompson5910

do you agree with the drawing so far?

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## More answers

- anonymous

Yes I do

- jim_thompson5910

these angles are congruent
|dw:1441673560035:dw|
since they are alternate interior angles and we have a pair of parallel lines

- jim_thompson5910

so in a sense, we have this triangle
|dw:1441673599603:dw|

- jim_thompson5910

do you know how to find x ?

- anonymous

no

- jim_thompson5910

have you learned of trig functions in your lessons?

- anonymous

No, this is a random question given in a summer assignement, I think I may know, but its better to just explain it to me with the steps

- jim_thompson5910

oh it's part of a summer worksheet? If you don't know the answer, then it's ok to leave it blank. The teacher wants to see where you are in terms of your math skills. If you don't know the answer, then the teacher knows where to focus the lesson. This will avoid him teaching you things you already know.

- anonymous

Still I wanna know, its being counted as a grade

- jim_thompson5910

that hardly seems fair to ask you a question you haven't learned about yet, and have it graded

- jim_thompson5910

is this for geometry or trig class?

- anonymous

trig class, pls just answer the question

- jim_thompson5910

take a look at this chart
http://passyworldofmathematics.com/Images/pwmImagesSix/TrigRatiosSeven550x398JPG.jpg
which two sides are we using?

- anonymous

adjacent and opp?

- jim_thompson5910

no, opp and hyp
look at the chart again and verify what I'm saying is correct
|dw:1441675548088:dw|

- jim_thompson5910

agreed? or no?

- anonymous

agree

- jim_thompson5910

which trig function uses opp and hyp together?

- anonymous

sin or soh as in from sohcahtoa

- jim_thompson5910

yes

- jim_thompson5910

so
sin(angle) = opp/hyp
sin(35) = x/4600

- jim_thompson5910

using a calculator, what is `sin(35)` equal to?

- anonymous

-0.42818266949

- jim_thompson5910

make sure you are in degree mode
what calculator do you have?

- anonymous

I just use google to calculate it, I dont have a graphing calculator..sorry can you get the result for it

- jim_thompson5910

use this calculator
http://web2.0calc.com/

- jim_thompson5910

try it again and tell me what you get for the value of `sin(35)`

- anonymous

0.573576436351

- jim_thompson5910

good

- jim_thompson5910

so `sin(35) = x/4600` is the same as `0.573576436351 = x/4600`

- jim_thompson5910

at this point, the trig stuff is gone and we have a normal algebraic equation
solve for x to get x = ??

- anonymous

-4599.426423563649?

- jim_thompson5910

idk how you got that

- jim_thompson5910

what steps did you do to get that?

- anonymous

I think that was wrong, but I have to get x by it self right. So i would need to subtract 4600- 0.573576436351

- jim_thompson5910

hint: undo division (what operation is the opposite of division?)

- anonymous

multiplication

- jim_thompson5910

yes

- jim_thompson5910

multiply both sides by ________ (fill in the blank)

- anonymous

4600? idk please help

- jim_thompson5910

yes, multiply both sides by 4600 to isolate x

- anonymous

I got x=2638.4516072146

- anonymous

But thats not one of the options

- jim_thompson5910

what are your options?

- anonymous

There

##### 1 Attachment

- jim_thompson5910

oh my bad, I mixed up opp and hyp and I'm just realizing that

- jim_thompson5910

sin(angle) = opp/hyp
sin(35) = 4600/x
0.573576436351 = 4600/x
0.573576436351*x = x*4600/x ... Multiply both sides by x.
0.573576436351*x = 4600
do you see how to isolate x?

- anonymous

in this case use 0.573576436351 to multiply on both sides?

- jim_thompson5910

you have to undo the multiplication in 0.573576436351*x

- anonymous

please demonstrate

- jim_thompson5910

what undoes multiplication?

- anonymous

division?

- jim_thompson5910

yes, you'll divide both sides by _______ (fill in the blank)

- anonymous

0.573576436351?

- jim_thompson5910

yes, divide both sides by that value

- anonymous

8019.8552598576954158?

- jim_thompson5910

correct, which rounds to 8019.86

- anonymous

Thanks mate :)

- jim_thompson5910

you're welcome

- anonymous

Can you help me with this one too: A large totem pole near Kalama, Washington,
is 154 ft tall. On a particular day at noon it
casts a 198 ft shadow. What is the sun's angle
of elevation at that time?

- anonymous

here are the options

##### 1 Attachment

- jim_thompson5910

are you able to draw a picture of the problem?

- anonymous

I am not, I cannot display it

- jim_thompson5910

how about on paper? are you able to draw out the triangle?

- anonymous

not really, I have no scanners, no tools on my pc nothing, I can still understand without a photo

- jim_thompson5910

no I mean just for you to see
you can describe the picture to me

- jim_thompson5910

draw out the triangle and then describe the picture

- anonymous

Yeah I cant see it, cause I dont understand how to draw it sorry

- jim_thompson5910

try to imagine what it would look like in real life
draw a vertical pole, then a shadow.
what forms?

- anonymous

okay totem pole at right (154 ft), and a shadow at the back of the pole which is 198 ft
, and the sun at the top of pole giving the shadow to pole

- jim_thompson5910

you should have this
|dw:1441679942494:dw|

- jim_thompson5910

which angle do they want? mark it on my drawing

- jim_thompson5910

click on the pencil to mark on my drawing

- anonymous

|dw:1441680351616:dw|

- anonymous

that one?

- jim_thompson5910

it's asking `What is the sun's angle of elevation at that time?`
the angle of elevation is actually this angle
|dw:1441680645165:dw|

- anonymous

ohh okay

- jim_thompson5910

look at that chart I posted above
which sides are the 154 and 196 with respect to that marked angle?

- anonymous

154=totem, and 198=shadow

- jim_thompson5910

I meant in terms of opp, hyp, adj

- anonymous

oh my bad, it would be: addj, and opp?

- jim_thompson5910

yeah
let's label our drawing with those
|dw:1441680960957:dw|

- jim_thompson5910

what trig function uses opp and adj?

- anonymous

tan

- jim_thompson5910

yep

- jim_thompson5910

tan(angle) = opp/adj
tan(x) = 154/198
I'm making the angle to be x for now

- jim_thompson5910

now you'll use that calculator I gave you above
and type in `arctan(154/198)`
the arctan function is the inverse of tangent. It helps find the angles

- anonymous

37.874983651098
?

- jim_thompson5910

correct

- jim_thompson5910

so the angle of elevation is approx 37.87 degrees

- anonymous

ahh okay thanks

- jim_thompson5910

you're welcome

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