 Hello and welcome to the session. I am Deepika here. Let's discuss a question, which says a contractor plans to install two slides for the children to play in a park. For the children below the age of five years, she prefers to have a slide whose top is at a height of 1.5 meter and is inclined at an angle of 30 degree to the ground. Whereas for elder children, she wants to have a steep slide at a height of 3 meter and inclined at an angle of 60 degree to the ground. What should be the length of the slide in each case? Let us first understand the trigonometric ratios of the angle C in right triangle ABC. So in right triangle ABC, we have Nc is equal to the side opposite to angle C upon hypotenuse that is AB upon AC. AC is equal to adjacent to angle C upon hypotenuse that is BC upon AC and Nc is equal to side opposite to angle C upon side adjacent to angle C that is AB upon BC. So this is the key idea behind that question. We will take the help of this key idea to solve the above question. So let's start the solution. First, let us draw a simple diagram to represent our given problem. This diagram represents a slide for the children below the age of five years. We will consider two cases. Now case one for children below the age of five years presents a slide whose top is at a height of 1.5 meter and is inclined at an angle of 30 degree to the ground. So we have AB is equal to 1.5 meter and angle ACB is equal to 30 degree. We want to find the length of the slide that is AC we have to find. Now to determine AC we choose a trigonometric ratio which involves both AB and AC. So according to our key idea we will choose a trigonometric ratio as sine 30 or cosecant 30 as these ratio involves AB and AC. So in right triangle ABC we have AB upon AC is equal to sine 30. AB is given to us 1.5 meter. So we have 1.5 upon AC is equal to 1 by 2 as sine 30 degrees 1 by 2. So on cross multiplying we get AC is equal to 3.0. This implies the length of this slide for children below five years is meter. Let us consider the second case for elder children is equal to 3 meter and angle ACB is equal to 60 degree. Again we have to find AC again in right triangle AB upon AC is equal to sine 60 degree. Now AB is 3 meter upon AC is equal to root 3 by 2 because sine 60 is root 3 by 2. So on cross multiplying we get AC is equal to into 2 upon root 3 is equal to multiply the numerator and the denominator by root 3. This is equal to 3 into 2 into root 3 upon 3. On cancellation we have 2 root 3 that is AC is equal to 2 root 3. Hence the length of this slide for elder children 3 meter. So for the above question is that the length of the slide for children below the age of 5 years is 3 meter. The length of the slide for elder children is equal to 2 root 3 meter. I hope the solution is clear to you. Bye and take care.