00:01
So, in the given question we are told that a very steep mountain is inclined 70 degrees from horizontal and rises to a height of 3 ,700 feet above the surrounding plane.
00:18
So if we assume that the mountain is like this, we are told that the incline of this mountain is 70 degrees and the height of this mountain.
00:30
Is 3 ,700 feet right yeah 3 ,700 feet above the ground and now we are told a billionaire wants to install a cable car to access his mountain top hideaway now one of the stations needs to be at the peak of the mountain which is over here and the other at a point of 970 away from the base of the mountain so let's say somewhere over here right that is 970 feet from the base of the mountain now we are told to find the shortest possible distance between these stations so we have to find the shortest possible distance between these two points so we can draw this as a right triangle the steep over here is 70 degrees now this point is the peak which is 3 ,700 feet away from the base and this point over here is the second station which is 970 970 feet away right and this point would be we can draw this point over here since this would be the place where the station would be right so let's write over here this is 970 this distance is 970 feet now we are told to find the shortest possible distance between these stations right which means we should find this distance this distance is what we need to find so let's take this as a right angled triangle right and then this angle would be 90 plus 70 is 160 160 when we subtract 160 from 180 which is the all interior angles we would get an angle of 20 degree over here now what we could do is we can draw two triangles over here right so this is a smaller triangle with the same angle of 70 degrees and the height of 970 feet over here and what we can do is we can first find a this distance over here that is let's name this triangle p this is station 1 so s this is the base and this let's say is a point called oh right so now this would be this is the point so now in the triangle a b s this is 70 degrees and this height vertical height is 970 feet so when we take the sign of the angle 70 degrees what we could do in a right angled triangle is to take the length of the opposite side to sign of 70 degrees uh opposite side to the angle 70 degrees and divide this with with the length of the hypotenuse right so so from this we can find the length of the hypotenuse as 970 divided by sign of 70 degrees.
04:45
So when we take 970 and divide it with the sign of 70 degrees, what we would get as the answer is 130.
05:07
To 5 feet and now that we have the hypotenuse of abs as 1 ,300, 132 feet let's move on to the bigger triangle the bigger triangle which is bpo with the same angle of 70 degrees and a vertical distance of 3 ,700 feet and the same way over here we can find the hypotenuse p b by taking 3 ,700 feet divided by the sign of 70 degrees so when we take 3 ,700 feet and divide it with the sign of 70 degrees so when we take 3 ,700, 3 ,700 feet and divide it with the sign of 70 degrees what we would have as the answer is 3 ,900 and 37 .35 feet.
06:22
Now we have the distance of a p b which is 3 ,937 .45 and we have s b and we have s b and which is 132 .25.
06:44
So the required distance that we needed to find, the required distance is ps.
06:52
So the required distance, required distance, p s is pb minus s b...