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Ok So I understand tangents, sines, and cosines. But this night's homework isn't making ANY sense to me at all!!!! Like, I literally put a question mark down for every problem except 1... DALPE
Well, I guess I need to start out by saying THANKS FOR THE QUESTION!!!
The game you have to play here is simply "FIND THE TRIANGLE" (exciting, eh?... read pgs 317-318 to understand the terminology for angle of elevation and angle of depression... outside of that, there is NOTHING new in section 8-7).
In problem 3, the string of the kite is making a 40-degree angle with the ground below. We have to make a couple of assumptions here a) the ground is flat (so as to make a leg of a right triangle) and b) the string is measured to the "base" of the kite and we discount the size of the kite. As we all know, according to plane (Euclidean) geometry, the world is flat, so this should not be a problem.
To find the height of the kite, we drop an imaginary perpendicular line from the base of the kite to the ground. If you are drawing along with me, the 80ft string represents the hypotenuse, yes?
So, whadda-we-gotzk? We gotzk a right triangle with a 40 degree angle (included between the ground and the string) and an 80 ft hypotenuse. We want to find the length of the imaginary perp-line, which is OPPOSITE the 40-deg angle, yes? Hmmmm... which of the trig ratios involves the OPP and the HYP?
If you can do the problems on page 308 and 314, all you need to do is translate the stories into diagrams... the problems are the same.
If all of this didn't help: a) ask another question b) check out the video tutors on mathchamber... there are examples for both angle of elevation and angle of depression
Keep the cards and letters comin'... and lmk if this helped.
I agree with DALPE and i don't know what to do with #6. Also, i think i've been doing all of them wrong, i only used tangents, not sines or cosines. Another thing i didn't get is what is the grade they reffer to in #10? My last question is would your mom (who im pretty sure is the one in the hospital right?) be called mrs. chamberlain? -Natasha
Well, we'll go over all of these in class tomorrow... (btw your hw was #1-17 ODD) but here goes as for #6 anyway:
#6(re-phrased) An airplane is approaching an airport runway at a 3-degree angle of depression. Find the (assumed flat) ground distance it will have to travel if it begins it's descent from 30,000 ft (as we've already agreed, the earth is flat in our wonderful world of Euclidean geometry).
Once again, we need to FIND THE RIGHT TRIANGLE!! So, draw the plane at 30,000ft (let's have it traveling west to east - aka left to right - on our paper, ok?) and drop a perpendicular line to the ground. Our world starts there (and hint!... you just drew one leg of the right triangle that happens to measure 30,000 ft). The ground will be the other leg, you don't know how far but draw the ground anyway (to the right, right?). Now connect the "plane" vertex to the ground using an 87-degree angle (why 87?... you s/b able to tell me).
OK, so you have a triangle with three known angles AND you know one side length. You should see two options:
1) tan(87-degrees)= opp/30,000 or 2) tan(3-degrees) = 30,000/adj
Please remember folks... the trig ratios are just ratios... in order to make them useful in a proportion, YOU have to supply the other ratio, aka the lengths of two of the sides. If one of the sides is unknown, the proportion is the equation that let's you SOLVE... and as you recall from Algebra, your only havin' fun when your SOLVIN'!!
You select which ratio to use (Sine, Cosine, or Tangent) based on a) the side you know and b) the side you need to know.
And, yes, while I call her mom, at last check there are some that call her Mrs. Chamberlain.
Ok So I understand tangents, sines, and cosines. But this night's homework isn't making ANY sense to me at all!!!! Like, I literally put a question mark down for every problem except 1...
ReplyDeleteDALPE
Dear Strung-Out on South St,
ReplyDeleteWell, I guess I need to start out by saying THANKS FOR THE QUESTION!!!
The game you have to play here is simply "FIND THE TRIANGLE" (exciting, eh?... read pgs 317-318 to understand the terminology for angle of elevation and angle of depression... outside of that, there is NOTHING new in section 8-7).
In problem 3, the string of the kite is making a 40-degree angle with the ground below. We have to make a couple of assumptions here a) the ground is flat (so as to make a leg of a right triangle) and b) the string is measured to the "base" of the kite and we discount the size of the kite. As we all know, according to plane (Euclidean) geometry, the world is flat, so this should not be a problem.
To find the height of the kite, we drop an imaginary perpendicular line from the base of the kite to the ground. If you are drawing along with me, the 80ft string represents the hypotenuse, yes?
So, whadda-we-gotzk? We gotzk a right triangle with a 40 degree angle (included between the ground and the string) and an 80 ft hypotenuse. We want to find the length of the imaginary perp-line, which is OPPOSITE the 40-deg angle, yes? Hmmmm... which of the trig ratios involves the OPP and the HYP?
If you can do the problems on page 308 and 314, all you need to do is translate the stories into diagrams... the problems are the same.
If all of this didn't help:
a) ask another question
b) check out the video tutors on mathchamber... there are examples for both angle of elevation and angle of depression
Keep the cards and letters comin'... and lmk if this helped.
Mr. C.
PS to Conor: You intuitively know the answer to #13 (pg 320), but can you prove it geometrically?
ReplyDeleteI agree with DALPE and i don't know what to do with #6. Also, i think i've been doing all of them wrong, i only used tangents, not sines or cosines. Another thing i didn't get is what is the grade they reffer to in #10? My last question is would your mom (who im pretty sure is the one in the hospital right?) be called mrs. chamberlain?
ReplyDelete-Natasha
Well, we'll go over all of these in class tomorrow... (btw your hw was #1-17 ODD) but here goes as for #6 anyway:
ReplyDelete#6(re-phrased) An airplane is approaching an airport runway at a 3-degree angle of depression. Find the (assumed flat) ground distance it will have to travel if it begins it's descent from 30,000 ft (as we've already agreed, the earth is flat in our wonderful world of Euclidean geometry).
Once again, we need to FIND THE RIGHT TRIANGLE!! So, draw the plane at 30,000ft (let's have it traveling west to east - aka left to right - on our paper, ok?) and drop a perpendicular line to the ground. Our world starts there (and hint!... you just drew one leg of the right triangle that happens to measure 30,000 ft). The ground will be the other leg, you don't know how far but draw the ground anyway (to the right, right?). Now connect the "plane" vertex to the ground using an 87-degree angle (why 87?... you s/b able to tell me).
OK, so you have a triangle with three known angles AND you know one side length. You should see two options:
1) tan(87-degrees)= opp/30,000
or
2) tan(3-degrees) = 30,000/adj
Ca-peesh?!
Please remember folks... the trig ratios are just ratios... in order to make them useful in a proportion, YOU have to supply the other ratio, aka the lengths of two of the sides. If one of the sides is unknown, the proportion is the equation that let's you SOLVE... and as you recall from Algebra, your only havin' fun when your SOLVIN'!!
ReplyDeleteYou select which ratio to use (Sine, Cosine, or Tangent) based on
a) the side you know and
b) the side you need to know.
And, yes, while I call her mom, at last check there are some that call her Mrs. Chamberlain.
Mr. C.