Let a vertical tower AB have its end A on the level ground.  Let C be the mid-point of AB and P be a point on the ground such that AP=2AB.  If \angle BPC= \beta, then tan β is equal to :

 

  • Option 1)

    \frac{1}{4}

  • Option 2)

    \frac{2}{9}

  • Option 3)

    \frac{4}{9}

  • Option 4)

    \frac{6}{7}

 

Answers (1)

As we learnt in

Height and Distances -

The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

-

 Let, AC=CB=h, AB=2h and AP=4h

Now, \:\tan \angle BPA=\frac{2h}{4h}=\frac{1}{2}

\tan \angle CPA=\frac{h}{4h}=\frac{1}{4}

\tan \beta=\tan (\angle BPA- \angle CPA)=\frac{tan(\angle BPA)-\tan(\angle CPA)}{1+\tan(\angle BPA)\:\tan(\angle CPA)}

=\frac{\frac{1}{2}-\frac{1}{4}}{1+\frac{1}{8}}=\frac{\frac{1}{4}}{\frac{9}{8}}=\frac{2}{9}

\tan \beta=\frac{2}{9}

 


Option 1)

\frac{1}{4}

This option is incorrect.

Option 2)

\frac{2}{9}

This option is correct.

Option 3)

\frac{4}{9}

This option is incorrect.

Option 4)

\frac{6}{7}

This option is incorrect.

Most Viewed Questions

Preparation Products

Knockout JEE Main 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main 2021

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes(Classes will start from Last week of September), Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions