Question
The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in
The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in
m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?
Here, OC = Height of the unfinished tower AC = The height will be the finished tower's height In ΔOBC, tan 30° = OC/BC ⇒ 1/√3 = OC/78 [∵ tan 30° = 1/√3] ⇒ OC = 78/√3 ⇒ OC = (78 × √3)/(√3 × √3) = 26√3 .....(1) Let, the height of the tower will be raised (AO) = x In ΔABC, tan 60° = AC/BC ⇒ √3 = (OC + x)/78 [∵ tan 60° = √3] ⇒ x + OC = 78√3 ⇒ x + 26√3 = 78√3 ⇒ x = 78√3 - 26√3 = 52√3More Mensuration Questions
- The length and breadth of a rectangle are increased by 35% and 40% respectively. The increase in the area of the resulting rectangle will be:
- The circumference of a circle is equal to the perimeter of a rectangle whose length and breadth are in ratio 13:10, respectively. If the area of the rectan...
- A solid right circular cylinder of radius 5 cm and height 20 cm is melted and recast into solid spheres of radius 2.5 cm. How many such spheres can be made...
- If the numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then what is the numeri...
- The height of a triangle is equal to the perimeter of a square whose diagonal is 6√2 m and the base of the same triangle is equal to the side of a square w...
- Determine the slant height of a cone with a volume of 1,884 cm³ and a base radius of 15 cm. (Use π = 3.14)
- A rectangular floor of length 24 m and breadth 18 m is to be covered with square tiles of side 60 cm. If the cost of tiling is Rs. 15 per tile, find the to...
- The length of a rectangle is four times its breadth. If its length is increased by 20 cm. and breadth is increased by 30 cm, the area of the rectangle is i...
- A cylinder has a curved surface area of 616 cm² and its height is 14 cm. What will be the diameter of the cylinder?
- What is the difference between (in m2) the area of a circular field of radius 28 metres and area of a rectangular piece of land having its dimensions as 44...
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
Think You're Ready for RBI Grade B?
RBI Grade B 2026 Phase 1 Memory Based Paper
- 200 Questions with Detailed Solutions
- Section-wise Coverage (GA, English, Quant & Reasoning)