AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

From a point on the ground, the angle of elevation of the top of a tower is observed to be $60 °$ From a point $40 m$ vertically above the first point of observation, the angle of elevation of the top of the tower is $30 °$ ,then the height of the tower and its horizontal distance from the point of observation 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

203 m

, 50m

203 m

, 60 m

203 m

, 40m

203 m

, 30m

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that from a point on the ground, the angle of elevation of the top of a tower is observed to be

60 °

From a point

40 m

vertically above the first point of observation, the angle of elevation of the top of the tower is

30 °

.
Consider the diagram,
Question Image

We know,

tanθ = \frac{Perpendicular}{Base}

\tan 60 ° = \sqrt{3}

\tan 30 ° = \frac{1}{\sqrt{3}}

,
In triangle QAP,

\tan 60 ° = \frac{QP}{AP}

\Rightarrow \tan 60 ° = \frac{x + 40}{AP}

In triangle QBP,

\tan 30 ° = \frac{QR}{BR}

\Rightarrow \tan 30 ° = \frac{x}{BR}

Therefore,

AP = x + 40 tan 60 ° BR = x tan 30 °

As AP and BR are equal so equate the expression of both to each other and find x.

x + 40 tan 60 ° = x tan 30 ° ⇒ x + 40 3 = x 3 ⇒ 2 x = 40 ⇒ x = 20 m

Now,

h = 20 + 40 ⇒ h = 60 m

Again,

d = \frac{20}{\tan 30 °}

\Rightarrow d = \frac{20}{\frac{1}{\sqrt{3}}}

\Rightarrow d = 20 \sqrt{3} m

Distance between point and tower

203 m

and the height of the tower is 60 m.
Therefore, option 4 is correct.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!