From the top of a tower 100 m high, a man observes the angles of depression of two ships A and B on opposite sides of the tower as 45° and 38° respectively. If the foot of the tower and the ships are in the same horizontal line, find the distance between ships A and B to the nearest metre. Use mathematical tables.
Let CD be the tower, with C as its foot and D as its top.
CD = 100 m.
The angles of elevation from A and B equal the corresponding angles of depression.
Therefore, ∠A = 45° and ∠B = 38°.
In △ACD:
⇒ tan 45° = \frac{CD}{AC}
⇒ 1 = \frac{100}{AC}
⇒ AC = 100 m
In △BCD:
⇒ tan 38° = \frac{CD}{BC}
⇒ 0.7813 = \frac{100}{BC}
⇒ BC = \frac{100}{0.7813}
⇒ BC ≈ 127.99 m
Since the ships are on opposite sides:
⇒ AB = AC + BC
⇒ AB = 100 + 127.99
⇒ AB = 227.99 m
Therefore, the distance between the ships, to the nearest metre, is 228 m.
More ICSE Easy level questions
A flagpole is erected at the top of a building. The angle of elevation of the top and foot of the flagpole from a point 100 m away, on the same level as that of the foot of the building, are 33° and 31° respectively. Find the height of the flagpole. Give your answer correct to the nearest metre.
Prove that: (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
AB is a vertical tower 100 m from the foot of a 30-storey building CD. The angles of depression from C and E, where E is the midpoint of CD, are 35° and 14° respectively. Use mathematical tables, rounding required values to two decimal places. Find the height of: (a) tower AB. (b) building CD.
The angles of elevation of the top of a 100 m high tree from two points A and B on opposite sides of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.
In the given diagram, DE ∥ BC and AD : DB = 2 : 3. (a) Prove that: ΔADE ~ ΔABC and hence find DE : BC. (b) Prove: ΔDFE ~ ΔCFB. (c) Given, area of ΔDFE = 16 square units, find the area of ΔCFB.
A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as shown in the given diagram. The radius of each of the three solids is 7 cm and heights of each of the cone and the cylinder is 24 cm. Find : (a) the total surface area of the given solid. (b) the cost of painting the total surface at the rate of ₹ 0.50 per cm2.
Ms. Sushmita went to a fair and participated in a game. A box contained number cards numbered from 01 to 30. The prizes were awarded as follows: Prize Number on the card drawn at random is a Wall clock Perfect square Water bottle Even number which is also a multiple of 3 Purse Prime number Find the probability of winning: (a) a wall clock. (b) a water bottle. (c) a purse.
In the given figure ‘O’ is the centre of the circle. PQ is a tangent to the circle at B and AB = AC. If ∠CBQ = 40°, find the unknown angles x, y, z and w.
The given figure shows an eye-drop bottle consisting of a hemispherical part and a cylindrical part, with a conical cap. The height of the cylindrical part and the height of the conical cap are each equal to the diameter, 7 cm. (a) Find the minimum height of a cylindrical box in which the bottle can be packed. (b) Find the volume of the liquid medicine that the bottle can contain. Use π = 22/7.
The difference of two natural numbers is 5 and sum of their reciprocals is . Find the two numbers.
Asha buys ₹ 20 shares of a company which pays 9% dividend at such a price that she gets a return of 12% on her investment. At what price did she buy each share? (a) ₹ 20 (b) ₹ 15 (c) ₹ 25 (d) ₹ 18
If A = , then A² is equal to: (a) (b) (c) (d)
