Two pillars of equal heights are at the point A and B on the opposite side of the road which is 120 m wide. From a point C on the line joining the foots of the pillars, the angle of elevation of the top of the pillar at A and B are 60° and 30° respectively. Find AC.
WBBSE
Class X
Mathematics
Application of Trigonometric Ratios
05 Mark
2024
Let the common height of the two pillars be h.
Let AC = x. Then CB = 120−x.
In Δ ACD
tan 30° = h\over x
⇒ h = x tan 30° = x\over √3
In Δ BCE
tan 60° = h\over 120 - x
⇒ √3 = {x\over √3}\over 120 - x
⇒ √3 = x\over √3(120 - x)
⇒ √3 × √3(120 – x) = x
⇒ 3 (120 – x) = x
⇒ 360 – 3x = x
⇒ 360 = 4x
⇒ x = 360\over 4 = 90 m
∴ AC = 90 m
Related Questions
More WBBSE Moderate level questions
1/12
Q.
The angle of elevation of the top of a pillar of height h from two...
A.
Let the height of the pillar be h. Let the horizontal distances...
Q.
Distance between two pillars is 150 m, height of one pillar is three times the...
A.
Let the height of the smaller pillar be h meters Then, the...
Q.
From the middle of a ground Habu observes a flying bird toward north at an...
A.
Let the initial position of the bird be A and the final...
Q.
From the roof of the building the angle of depression of the top and foot...
A.
In ΔEDC, tan 30° = or, = --- (1) In ΔEAB, tan...
Q.
Angle of elevation of the top of an incomplete tower from a point at a...
A.
In ΔABO tan 30° = or, = or, AB = = 28.86...
Q.
Prove that in any circle, angles in the same segment are equal.
A.
Given: Let ∠ACB and ∠ADB be any two angles in the segment...
Q.
Aman has taken a loan of Rs. 25,000 for 3 years, in such a way...
A.
Principal (P) = ₹ 25,000 Rate (r) = 4%, 5% and 6%...
Q.
After retirement Gobinda Babu got ₹ 5,00,000. He deposited a part of it in post...
A.
Let post office deposit = x and bank deposit = 500000 −...
Q.
Find the median of the data from the following distribution
A.
Class int Class boundary frequency (f) CF 0 - 9 0 -...
Q.
Find the mode from the following data
A.
The class with the highest frequency is 20 – 25, so it...
Q.
If 75 buckets of water of equal measure are taken out from the water of...
A.
Side of cube = 1.5 m Volume of the tank = (1.5)³...
Q.
Difference of outer and inner curved surface area of a hollow cylindrical pipe is 44...
A.
Let the outer radius = R and length (h) = 14 cm...