CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60 at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30. The height of the tower is

A
2a3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
23a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
a3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C a3

Let us consider the height of the tower as h
We know that, h=ACtan30=BCtan30 ...(1)


We know that AC=BC [ radius of circle]

Hence, we can say that ABC is an isosceles triangle with AC=BC.
So, ABC=BAC ...(2)

But ACB=60 [given]
ABC+BAC+ACB=180
ABC+ABC+60=180 [from (2)]
2×ABC=120
ABC=BAC=60

Hence ABC is an equilateral triangle.

AB=BC=CA=a ...(3)


h=atan30 [form equation (1)]
=a3

1313031_40828_ans_4b75b9a1ba7547f29af3f270334a9bdf.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle of Elevation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon