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The angles of depression of the top and bottom of a building 50 metres high as observed from the top of a tower are 30° and 60°, respectively. Find the height of the tower and also the horizontal distance between the building and the tower.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

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Question 28 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2
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Transcript

Question 28 The angles of depression of the top and bottom of a building 50 metres high as observed from the top of a tower are 30 and 60 , respectively. Find the height of the tower and also the horizontal distance between the building and the tower. Let building be AB & tower be CD Height of building = AB = 50 m Let, Height of tower = PC And, distance between tower and building = AC Angle of depression to top of building = QDB = 30 Angle of depression to bottom of building = QDA = 60 We have to find height of tower i.e. CD And distance between tower &building i.e. AC Draw BE parallel to AC & DQ Lines DQ & BE are parallel, And BD is the transversal DBE = QDB DBE = 30 Now, AC and BE are parallel lines. So, AC = BE Lines DQ & AC are parallel, And AD is the transversal DAC = QDA DAC = 45 Similarly, AB and CE are also parallel lines. So, CD = AB CD = 50 m Also, Since DC is perpendicular AC DEB = DCA = 90 In right angle triangle DBE tan B = ( )/(Side " " ) tan B = (" " )/ tan 30 = / 1/ 3 = (" " )/ BE = DE 3 In right angle triangle PAC tan A = ( " " )/( " " ) tan 60 = (" " )/ 3 = (" " )/ AC = (" " )/ 3 "BE = " (" " )/ 3 From (1) & (2) DE 3 = (" " )/ 3 DE 3 3 = DC 3DE = DC 3DE = DE + EC 3DE DE = EC 2DE = EC 2DE = 50 DE = 50/2 DE = 25 m Height of tower = DC = DE + EC = 25 + 50 = 75 m From (1) BE = DE 3 Putting DE = 25 BE = 25 3 m So, AC = BE = 25 3 m Distance between two buildings = AC = 25 m

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.