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

At the foot of a mountain, the elevation of its summit is $450$ . After ascending $1000 m$ towards the mountain up a slope of $30 °$ inclination, the elevation is found to be $60 °$ . Find the height of the mountain.

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

1336 m

1316 m

1323 m

1366 m

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that, at the foot of a mountain, the elevation of its summit is

450

.
We have to find the height of the mountain.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for

tan θ

tan θ = opposite adjacent .

Suppose, A and B be the first and second positions of observation, and PQ be the height of the mountain.
Then,

A B = 1000 m ⇒ A B = 1 km

The required figure geometry is shown in the figure below,
Question Image

Then by using the figure geometry,

∠ B A P = ∠ M A P − ∠ M A B ⇒ ∠ B A P = 45 ° − 30 ° ⇒ ∠ B A P = 15 °

∠ A P B = ∠ A P N − ∠ B P N ⇒ ∠ A P B = 45 ° − 90 − 60 ° ⇒ ∠ A P B = 45 ° − 30 ° ⇒ ∠ A P B = 15 °

Therefore,

△ A B P

is an isosceles triangle and

A B = B P = 1 km

. Thus,

P Q = P N + B M ⇒ P Q = B P sin 60 ° + A B sin 30 ° ⇒ P Q = 132 + 112 ⇒ P Q = 3 + 1 2 k m ⇒ P Q = 1.366 k m ⇒ P Q = 1366 m [1m=1000km]

The height of the mountain is 1366m.
Therefore, 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!