00:01
In the given question we are told that there is a building that is casting a shadow which is a hundred and twenty -eight feet long and at the same time a flagpole is casting a shadow that is 32 feet long.
00:19
Now the height of the flagpole is given to us as 24 feet and we are told to find the height of the building.
00:28
So what we could do over here is we can consider this as a right angled triangle, right? this over here can be considered as a right angled triangle and over here we can make a right angled triangle with the building and its shadow as well.
00:46
Now these two angles are the same because the sun is subtending the same angle on the flagpole and the building, right? so what we could do first is to find this angle over here, that is theta, and then we can use this angle, the same angle over here, to find the height of the building over here.
01:09
So to do this, we have to use a trigonometric ratio, which is, so let's consider a small triangle over here, a right angled triangle with length of sides a, b, and c.
01:25
Now the length of the hypodontines over here is c units, right? now let's consider an angle phi over here.
01:32
And now we can use some symbol relations in this triangle to find different trigonometric ratios.
01:40
So, for example, if we were to take the sign of the angle phi, what we could do is we could find the length of the opposite side to the angle phi and divide it with the length of the hypotenuse of this triangle.
01:57
So if you do this you will get the value of sign of the angle phi.
02:01
So over here what we can see is that the length of the side that is opposite to the angle phi is having a length of a units and the length of the triangle which is the length of the hypotenuse of the triangle is c units.
02:19
So a by c would give us the value of sign phi so similarly, we can also take the angle value, the value of the trigonometric ratio, tan phi, by using the ratio the length of the opposite side to the angle phi divided by the length of the adjacent side to the angle phi.
02:43
So in this case, the opposite side is still a, the opposite side to the angle phi is still a and the adjacent side to the angle phi would be the side which is having a length of b units...