Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Heights and Distances

NDA 2014 · Mathematics · Heights and Distances

A lamp post stands on a horizontal plane. From a point situated at...

A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is 30∘30^{{}^{\circ}}. What is the height of the lamp post?

Options

  1. A50 m
  2. B503m50 \sqrt{3} \mathrm{ m}
  3. C503m\frac{50}{\sqrt{3}} \mathrm{ m}
  4. D100 m

Correct answer

B. 503m50 \sqrt{3} \mathrm{ m}

Step-by-step solution


tan⁡30∘=h15013=h150\begin{aligned} \tan 30^{{}^{\circ}} & =\frac{h}{150} \\ \frac{1}{\sqrt{3}} & =\frac{h}{150}\end{aligned}\Rightarrow \quad h=\frac{150}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=50 \sqrt{3} \mathrm{ m}\thereforeHeightofthelamppostHeight of the lamp post=50 \sqrt{3} \mathrm{ m}$.
Practice Heights and Distances on Quantrex Academy →

More from Heights and Distances

A plane is observed to be approaching the airport. It is at a distance of 10 km from the… NDA 2026Consider the following for the two (02) items that follow: The top (M ) of a tower is… NDA 2025A man at M , standing 100 m away from the base (P ) of a chimney of height 50 m, observes… NDA 2025Consider the following for the two (02) items that follow: The top (M ) of a tower is… NDA 2025Paragraph: A flagstaff 20 m long standing on a pillar 10 m high subtends an angle ^ -1… NDA 2023Paragraph: There are two points P and Q due south of a leaning tower, which leans towards… NDA 2022Paragraph: There are two points P and Q due south of a leaning tower, which leans towards… NDA 2022A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff… NDA 2022Paragraph: There are two points P and Q due south of a leaning tower, which leans towards… NDA 2022A ladder 6 m long reaches a point 6 m below the top of a vertical flagstaff. From the… NDA 2021The shadow of a tower is found to be x metre longer, when the angle of elevation of the… NDA 2021The angle of elevation of a tower of height h from a point A due South of it is x and… NDA 2019A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the… NDA 2019A balloon is directly above one end of a bridge. The angle of depression of the other end… NDA 2018The top of a hill observed from the top and bottom of a building of height h is at angles… NDA 2018If a flag-staff of 6 m height placed on the top of a tower throws a shadow of 2 3 m along… NDA 2018 Full Heights and Distances list Heights and Distances JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs