Question

From a tower 126 m high, the angles of depression of two rocks which are in a horizontal
line through the base of the tower are 160 and 12° 20'. Find the distance between the
rocks if they are on
(i) the same side of the tower
(ii) the opposite sides of the tower.​

Answer 1

Answer:

Consider CD as the tower of height = 126m

A and B are the two rocks on the same line,

Angle of depression are 16

0

and 12

0

20

′

In triangle CAD,

tanθ=CD/AD

Substituting the values,

tan16

0

=126/x

0.2867=126/x

So, we get

x=126/0.2867

x=439.48

In right triangle CBD

tan12

0

20

′

=126/y

So, we get

0.2186=126/y

y=126/0.2186=576.40

(i) In the First case,

On the same side of the tower,

AB=BD−AD

AB=y−x

Substituting the values,

AB=576.40−439.48

AB=136.92m

(ii) In the second case,

On the opposite side of the tower,

AB=BD+AD

AB=y+x

Substituting the values,

AB=576.40+439.48

AB=1015.88m

solution

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