WEBVTT
1
00:00:00.340 --> 00:00:02.319 A:middle L:90%
So we give it another interesting problem. We're told
2
00:00:02.319 --> 00:00:06.379 A:middle L:90%
to inscribe a rectangle of base be based B and
3
00:00:06.379 --> 00:00:09.609 A:middle L:90%
high H height age in a circle of radius one
4
00:00:09.619 --> 00:00:13.410 A:middle L:90%
in a circle with a radius of one and inscribe
5
00:00:13.410 --> 00:00:15.189 A:middle L:90%
. And I saw. So these triangle in a
6
00:00:15.189 --> 00:00:17.690 A:middle L:90%
region of the circle cut off by one of the
7
00:00:17.690 --> 00:00:22.089 A:middle L:90%
base rectangles by one base of the rectangle and that
8
00:00:22.089 --> 00:00:25.730 A:middle L:90%
side eyes to be a basic triangle. For what
9
00:00:25.730 --> 00:00:27.679 A:middle L:90%
value of Asia. The rectangle and trying will have
10
00:00:27.679 --> 00:00:32.170 A:middle L:90%
the same exact area. Okay, so we know
11
00:00:32.170 --> 00:00:36.539 A:middle L:90%
that um the rectangle our will call this. Here
12
00:00:36.539 --> 00:00:40.890 A:middle L:90%
we go. The wreck tangle. We could denote
13
00:00:40.890 --> 00:00:44.789 A:middle L:90%
by saying s wrecked For the surveyor of the rectangle
14
00:00:44.829 --> 00:00:47.859 A:middle L:90%
is equal to base times height, right? And
15
00:00:47.859 --> 00:00:51.750 A:middle L:90%
we know that the triangle area Try a gold.
16
00:00:52.759 --> 00:00:55.539 A:middle L:90%
Ah, we don't. You know by s Trig
17
00:00:56.710 --> 00:01:00.670 A:middle L:90%
is equal to or a stage s try. Let's
18
00:01:00.670 --> 00:01:04.799 A:middle L:90%
try. I equal to base times one minus h
19
00:01:04.810 --> 00:01:08.620 A:middle L:90%
over too. Over to So the air. The
20
00:01:08.620 --> 00:01:11.269 A:middle L:90%
right thing was easy. The area of the triangle
21
00:01:11.269 --> 00:01:12.599 A:middle L:90%
is there more tricky. We have the base of
22
00:01:12.599 --> 00:01:15.480 A:middle L:90%
the triangle. So if you manage to figure out
23
00:01:15.480 --> 00:01:18.439 A:middle L:90%
the height that we can use. The formula of
24
00:01:18.450 --> 00:01:21.049 A:middle L:90%
s triangle is equal to base times height over too
25
00:01:21.640 --> 00:01:23.299 A:middle L:90%
. So if we draw a line in the center
26
00:01:23.299 --> 00:01:25.569 A:middle L:90%
of the rectangle which is also center of the circle
27
00:01:25.569 --> 00:01:27.750 A:middle L:90%
to the top of the triangle, the distances are
28
00:01:29.239 --> 00:01:30.170 A:middle L:90%
right. This is the radius and ours. You
29
00:01:30.170 --> 00:01:34.299 A:middle L:90%
goto what? To get the height of the triangle
30
00:01:34.299 --> 00:01:36.379 A:middle L:90%
. We need subtract from the height of the part
31
00:01:36.379 --> 00:01:38.730 A:middle L:90%
of the line we drew in the rectangles. That's
32
00:01:38.760 --> 00:01:41.439 A:middle L:90%
h over to. Thus, the height of the
33
00:01:41.439 --> 00:01:44.340 A:middle L:90%
triangle is one minus h over to which is what
34
00:01:44.340 --> 00:01:46.629 A:middle L:90%
I used right here. So we can say at
35
00:01:46.629 --> 00:01:49.799 A:middle L:90%
the surface area of the triangle, triangle is able
36
00:01:49.799 --> 00:01:52.709 A:middle L:90%
to base times one minus age or two over too
37
00:01:53.030 --> 00:01:56.150 A:middle L:90%
. So now that we determine the proper for most
38
00:01:56.150 --> 00:01:57.840 A:middle L:90%
of the area, we need to find the value
39
00:01:57.840 --> 00:02:00.239 A:middle L:90%
of H for which they're equal. So we're gonna
40
00:02:00.239 --> 00:02:01.939 A:middle L:90%
go ahead and solve the obtained equation for age.
41
00:02:02.180 --> 00:02:04.530 A:middle L:90%
So we're gonna go ahead and do this on the
42
00:02:04.530 --> 00:02:08.729 A:middle L:90%
next page. So we're to say base times height
43
00:02:08.729 --> 00:02:12.639 A:middle L:90%
is equal. Do base times one minus h over
44
00:02:12.639 --> 00:02:15.280 A:middle L:90%
too. All over too. So we say okay
45
00:02:15.280 --> 00:02:19.250 A:middle L:90%
to ages equal do one minus H over too,
46
00:02:19.939 --> 00:02:22.860 A:middle L:90%
and to age plus h over to is eagle toe
47
00:02:22.860 --> 00:02:24.870 A:middle L:90%
one. Thus, five over to H is equal
48
00:02:24.870 --> 00:02:29.479 A:middle L:90%
to one thus ages equal to two over five or
49
00:02:29.479 --> 00:02:34.590 A:middle L:90%
2/5 and that is our answer. H is equal
50
00:02:34.590 --> 00:02:35.810 A:middle L:90%
to 2/5.