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 ?

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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 ?

Mathematics
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|dw:1441671957196:dw|
|dw:1441671998905:dw|
do you agree with the drawing so far?

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Other answers:

Yes I do
these angles are congruent |dw:1441673560035:dw| since they are alternate interior angles and we have a pair of parallel lines
so in a sense, we have this triangle |dw:1441673599603:dw|
do you know how to find x ?
no
have you learned of trig functions in your lessons?
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
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.
Still I wanna know, its being counted as a grade
that hardly seems fair to ask you a question you haven't learned about yet, and have it graded
is this for geometry or trig class?
trig class, pls just answer the question
take a look at this chart http://passyworldofmathematics.com/Images/pwmImagesSix/TrigRatiosSeven550x398JPG.jpg which two sides are we using?
adjacent and opp?
no, opp and hyp look at the chart again and verify what I'm saying is correct |dw:1441675548088:dw|
agreed? or no?
agree
which trig function uses opp and hyp together?
sin or soh as in from sohcahtoa
yes
so sin(angle) = opp/hyp sin(35) = x/4600
using a calculator, what is `sin(35)` equal to?
-0.42818266949
make sure you are in degree mode what calculator do you have?
I just use google to calculate it, I dont have a graphing calculator..sorry can you get the result for it
use this calculator http://web2.0calc.com/
try it again and tell me what you get for the value of `sin(35)`
0.573576436351
good
so `sin(35) = x/4600` is the same as `0.573576436351 = x/4600`
at this point, the trig stuff is gone and we have a normal algebraic equation solve for x to get x = ??
-4599.426423563649?
idk how you got that
what steps did you do to get that?
I think that was wrong, but I have to get x by it self right. So i would need to subtract 4600- 0.573576436351
hint: undo division (what operation is the opposite of division?)
multiplication
yes
multiply both sides by ________ (fill in the blank)
4600? idk please help
yes, multiply both sides by 4600 to isolate x
I got x=2638.4516072146
But thats not one of the options
what are your options?
There
1 Attachment
oh my bad, I mixed up opp and hyp and I'm just realizing that
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?
in this case use 0.573576436351 to multiply on both sides?
you have to undo the multiplication in 0.573576436351*x
please demonstrate
what undoes multiplication?
division?
yes, you'll divide both sides by _______ (fill in the blank)
0.573576436351?
yes, divide both sides by that value
8019.8552598576954158?
correct, which rounds to 8019.86
Thanks mate :)
you're welcome
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?
here are the options
1 Attachment
are you able to draw a picture of the problem?
I am not, I cannot display it
how about on paper? are you able to draw out the triangle?
not really, I have no scanners, no tools on my pc nothing, I can still understand without a photo
no I mean just for you to see you can describe the picture to me
draw out the triangle and then describe the picture
Yeah I cant see it, cause I dont understand how to draw it sorry
try to imagine what it would look like in real life draw a vertical pole, then a shadow. what forms?
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
you should have this |dw:1441679942494:dw|
which angle do they want? mark it on my drawing
click on the pencil to mark on my drawing
|dw:1441680351616:dw|
that one?
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|
ohh okay
look at that chart I posted above which sides are the 154 and 196 with respect to that marked angle?
154=totem, and 198=shadow
I meant in terms of opp, hyp, adj
oh my bad, it would be: addj, and opp?
yeah let's label our drawing with those |dw:1441680960957:dw|
what trig function uses opp and adj?
tan
yep
tan(angle) = opp/adj tan(x) = 154/198 I'm making the angle to be x for now
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
37.874983651098 ?
correct
so the angle of elevation is approx 37.87 degrees
ahh okay thanks
you're welcome

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