00:01
Two ships leave port.
00:02
Ship x is traveling due north, and ship y is heading due east.
00:13
13 hours later, they are 650 miles apart.
00:23
Ship x had traveled 520 miles.
00:28
We want to know how many miles ship y traveled.
00:33
Well, if one is going due north and the other is going due east, east, that's making a 90 degree angle.
00:40
So we can use pythagorean theorem.
00:43
520 squared plus y squared equals 650 squared.
00:50
So y squared is 650 squared minus 520 squared.
00:59
Let's grab a calculator.
01:01
650 squared minus 520 squared is going to give me 152100.
01:10
Take the square root and you get 390 so that ship traveled 390 miles now in number eight we're told that we have a rectangular soccer field that's 120 meters long and 90 meters wide the coach asks the players to run from one corner to the other corner diagonally so in other words we want to just find the diagonal.
01:49
Again, it's a rectangle.
01:52
It has a right angle.
01:54
Pythagorean theorem will solve for us.
01:58
90 squared plus 120 squared.
02:02
That's 22500.
02:06
Take the square root.
02:08
The diagonal is 150 meters.
02:20
I have an isosceles triangle.
02:23
So an isosceles triangle is a triangle with, two congruent sides.
02:29
They measure 20 centimeters each.
02:32
The base is 10.
02:37
I want the area.
02:40
To find the area, i need the base and i also need a height.
02:48
So i know the altitude, nisosceles triangle is going to split that base in half.
02:54
So i can use pythagorean theorem to find the height.
02:58
5 squared plus h squared.
03:01
Equals 20 squared.
03:08
So h squared is 375.
03:16
H is the square root of 375, which is 5 radical 15.
03:29
Area is going to be half of the base, which is 10 times the height, 5 radical 15.
03:39
So that's 25 radical 15.
03:45
If you need an approximation, 98 .825...