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The School of Athens
Euclid, as imagined by Raphael in this detail from The School of Athens.
Jamshed Al-Kashi
Al-Kashi was one of the greatest mathematicians of the 15th century, calculating the sin(1*) correct to 16 decimal places.
Al-Beruni
The 11th century scientist and philosopher managed to estimate the radius of the earth using a very creative method that employed trigonometry.
21 comments:
Howdy,
I've been thinking of ways to do number one on the test and may have found a way.... I was thinking, maybe if you proved that the two triangles, one being the lamp height, it's light beam on the ground and the other being the man's height and his shadow are similar you could find the distance of the man from the light. Do any of y'all have any thoughts on where to start?
Vranian
I'm having a little trouble with the diagram... Is it basically just a smaller right triangle inside of a bigger right triangle?
That's what I see too, Sam.
Woah, can you believe it? The two sophomore boys were the first of ANYONE to post? Wow, that's ironic.
Mr. Kerai i was wondering if we could possibly have this takehome test due monday because i literally had no time this weekend because Friday and Saturday i had Model UN until like eleven and sunday i joined my church and afterwards i was overwhelmed with homework. I was just wondering if it is at all possible to get a little extension on the test, but only if you want to.
Jack M
^^That is a wonderful idea Jack!^^
Steven, it was pretty simple to prove the similarity with three = angles, but where have you gone form there?
i'm not Steven, but I think you can use the ratio of similtude, which is the lightpole divided by the man's height, to find the length of ground (base of larger right triangle)
if all three ANGLES are similar then bc AND WHATEVer you called the other line are // parallel how do you find the similarity of the trIANGLES sorry about the caps
this problem befuddles me from the description i still dont understand the diagram can anyone help? like were is the light in comparison to the man and his shadow???
Jack
If the light, the point below the light, and the end of the man's shadow creates a triangle, the light is the top of the triangle, the line from the light to the point below is perpendicular to the plane of the ground and to the line from that point to the end of the man's shadow
A
/I
/ I
/ I
/ /I E
/ / I
C / / I C
--------
F
Does this look right at all like A is the light and EC is the man and his shadow is CF?
um that didnt turn out right lemme try again
B
II
I I
I I
EII I
I I I
I I I
A ------- C
F
Ok this is the new one. Its the diagram:
Does this look right at all like A is the light and EC is the man and his shadow is CF?
A
|.\
|..\
|...\
|....\
|.....\
|......\
|.......\
|........\
|.........\
B----------C
a=light
b=point below light
c=man's shadow's end
ok delete those posts. What is going on. they don't come out right
Blogger ignores unnecessary spaces
all right thank you. so from where to where are we trying to find
someone said something earlier about two triangles
we are trying to find the distance from B to E (see diagramme)E is the man's feet
A
|.\
|..\
|...\
|....\
|.....\
|......\
B----E--C
is there a point above E on line AC that is perpindicular to BC
Light
A
..
...
....
.....
......
.......
........
........M.
........A..
........A...
........A....
E.......N....F
AE is the perpendicular of the shadow to the ground which is twenty feet. the Maaan is the perpendicular on the hypotenuse of AFE which is 6 feet, and then NF is 9 feet. We had to find EN for this problem. The two triagnles that the boys were talking about earlier are the similar triangles AEF and MNF.
I hope this closes up any confusion...
ok yea now i completely understand. i dont know how i got so confused thank you michael and scott
jack m
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