 Hello and welcome to the session. In this session we discuss the following question which says two poles 15 meter and 20 meter high stand upright in a playground if their feet are 12 meter apart find the distance between their tops. First let's recall the Pythagoras theorem according to this we have that in a right triangle the square of the hypotenuse equals the sum of the squares of its remaining two sides. This is the key idea of this question. Let's move on to the solution now. We take let ad be a pole such that we have ad is equal to 15 meters so this ad is of length 15 meters then let bc be a pole such that bc is equal to 20 meters so this per bc is of height 20 meters. In the question we have that their feet are 12 meter apart so we have ad is equal to 12 meters we need to find the distance between their tops that is we need to find cd. So first of all from d we draw dl perpendicular to bc so this dl is perpendicular to bc. Now as you can see that bc is 20 meters and ad is 15 meters so obviously bl would also be 15 meters. Now from the figure we have bc is equal to bl plus lc so this means lc is equal to bc minus bl that is we have lc is equal to 20 minus 15 meters so this gives lc is equal to 5 meters. In the same way we also have ad is equal to dl is equal to 12 meters so in right triangle dlc we have dc square is equal to dl square plus lc square this is by the Pythagoras theorem that we have already stated that in a right triangle the square of the hypotenuse is equal to sum of the squares of the remaining two sides so we get dc square is equal to now dl is equal to 12 meters so this is equal to 12 square plus lc square which is 5 meters so plus 5 square that is dc square is equal to 144 plus 25 so we have dc square is equal to 169 which means that dc is equal to square root of 169 which is equal to 13 therefore we get dc or you can say cd is equal to 13 meters which is the distance between the tops of the two poles so therefore the distance between the tops of the two poles is 13 meters so 13 meters is our final answer this completes the session hope you have understood the solution for this question.