Question 28 - CBSE Class 10 Sample Paper for 2018 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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.

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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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