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

On the same side of a tower two objects are located. The angle of elevation of the top of the tower from the objects are ${45 °}^{}$ and ${60 °}^{}$ . If the height of the tower is $150 m$ , the distance between the objects 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

63.5

76.9

86.7

90

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that the angle of elevation of the top of the tower from the objects are

{45 °}^{}

and

{60 °}^{}

. The height of the tower is

150 m

.
According to the given data, the figure has been drawn below.
Question Image

Let

AB

be the tower and

C

and

D

be the point of the object.
From the figure,

AB = 150 m

and

∠ ACB = {45 °}^{}

and

∠ ADB = {60 °}^{}

.
In

ΔBAD

tan θ = P e r p e n d i c u l a r b a s e

\tan {60 °}^{} = \frac{AB}{AD}

\Rightarrow \sqrt{3} = \frac{150}{AD}

(\tan 60 ° = \sqrt{3})

\Rightarrow AD = \frac{150}{\sqrt{3}} m

In triangle

ΔBAC

tan θ = P e r p e n d i c u l a r b a s e

\tan {45 °}^{} = \frac{AB}{AC}

\Rightarrow 1 = \frac{150}{AC}

(\tan 45 ° = 1)

\Rightarrow AC = 150 m

∴ CD = AC - AD

\Rightarrow 150 - \frac{150}{\sqrt{3}}

\Rightarrow [\frac{150 (\sqrt{3} - 1)}{\sqrt{3}}]

Multiply the numerator and denominator by

(\sqrt{3})

\Rightarrow \frac{150 (\sqrt{3} - 1) \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}

\Rightarrow 50 (3 - \sqrt{3})

\Rightarrow 50 \times 1.27

\Rightarrow 63.5 m

So, the correct option is 1.

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!