00:01
So the best approach to this problem is to probably draw a picture.
00:03
So we're told that we have a plane that's flying at an elevation of 31 ,000 feet.
00:08
So let's picture this is the ground.
00:10
So here's our airplane.
00:11
And i'm going to spare you from seeing my drawing, but i'm going to let you know that dot represents my airplane.
00:17
So if we're told that the elevation is 31 ,000 feet, that means the distance from our plane straight down to the ground.
00:23
So notice, it would make a right angle, would be 31 ,000 feet.
00:26
Okay, well, we're told that it is within sight of an airport, and the pilot finds the angle of depression to the airport is 19 degrees.
00:37
So let's say that this point right here, this would be our airport.
00:42
So when they say the angle of depression, that means their line of sight from the plane to the airport.
00:48
But what you have to be careful is the angle of depression means if i was to be looking straight, the angle between that straight looking and down to that line of sight.
00:57
This would be my 19 degree angle.
00:59
Well, how does that correspond to our triangle? well, because this line of sight is parallel to the line of the ground, this angle down here with the airport would be alternate interior angles with that angle of depression.
01:11
So now we know this bottom angle is 19 degrees.
01:14
Okay, so now they want us to find a distance between the plane and the airport.
01:18
Well, that would just be the hypotenuse for this triangle.
01:21
Well, because compared to our 90 degree angle, we know the opposite side and we want to find the hypotenuse, we can use our sign function to help us.
01:29
So we'll know that the sign of 19 degrees would be equal to the opposite side, 31 ,000, divided by the hypotenuse, which is x.
01:37
So now we just have to solve for x...