sir this is the important question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
it is given that From the top of a church spire 96 m high,
the angles of depression of two vehicles on a road,
at the same level as the base of the spire and on the same side of it are x0 and y0,
where tan x0 = ¼ and tan y0 = 1/7.
Calculate the distance between the vehicles
question no 20 , heights and distances , ICSE board
Consider CH as the height of the church
A and B are two vehicles which make an angle of depression x0 and y0 from C
Take AH = x and BH = y
In a right triangle CBH
tan x0 = CH/AH = 96/y
Substituting the values
1/4 = 96/y
So we get
y = 96 × 4 = 384 m
In right triangle CAH
tan y0 = CH/AH = 96/x
Substituting the values
1/7 = 96/x
So we get
x = 96 × 7 = 672 m
Here
AB = x – y
AB = 672 – 384
AB = 288 m