The angular depression of the top and foot of a tower as seen from the top of a second tower which is 150m high and standing on the same level as the first are $α$ and $β$ respectively. If $tan α = 43$ and $tan β = 52$ , then the distance between their top is:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

100m

120m

110m

130m

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

https://www.vedantu.com/question-sets/072f6118-abf8-4acc-b6fe-189bbf8232538683943630737818575.png

Now, ∠ FBD = ∠ BDE
This is because line BF is parallel to line DE and BD acts as transversal. The interior opposite angles formed by the transversal are equal.
∴ ∠ BDE = α
Similarly, ∠ FBC = ∠ BCA
Now, ABC is a triangle.
Let us consider that AC = y. Here y is the distance between the towers. Also, height of tower 2 = AB = 150m.
Now in Δ ABC

tan β = A B A C = 150 y

Also, we have given that

tan β = 52

∴ 150 y = 52 ⇒ 2 × 150 5 = 60

y = 60 m

Distance between the tower = 60m
Now in Δ BED, ∠ D = α and ∠ E = 90 degree.
So,

tan β = B E E D

Also, we have given that

tan α = 43

Therefore

B E E D = 43

Let us consider that BE = x
→ x is the height of tower 2 which is more than tower 1.

x E D = 43

DE is also the distance between the two towers.
∴ DE= AC = y = 60m
Therefore

x 60 = 43 ⇒ x = 4 × 60 3 = 80

x = 80 m

Now, the distance between the two towers is given by BD.
∴ BDE is a right angled triangle.
Where BE is perpendicular, BD is hypotenuses and ED is base.
By Pythagoras theorem,