MATHS Case study (4 Marks)

There exist a tower near the house of Shankar. The top of the tower AB is tied with steel wire and on the ground, it is tied with string support. One day Shankar tried to measure the longest of the wire AC using Pythagoras theorem.
(i) In the figure, the length of wire AC is: (take BC = 60 ft)
(ii) What is the area of ABC?
OR
What is the length of AP?
(iii) What is the area of a △POC?

Teewan, Arun and Pankaj were celebrating the festival of Diwali in open ground with firecrackers. There is a pedestal in the ground. All of sudden Teewan stands on a pedestal and releases a sky lantern from the top of the pedestal.

Based on the above information, answer the following questions.
(i) If the position of Pankaj is 25 m away from the base of the pedestal and Zr = 30°, then find the height of the pedestal.
(ii)If the vertical height of sky lantern from the top of pedestal is 12 m and∠y = 30°, then distance between Teewan and sky lantern ?
(iii) If ∠q = 60° and position of Arun is 15 m away from the base of pedestal, then find the height of pedestal.
OR
Which one is a pair of angles of depression?

There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing
on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take √3 = 1.73)

Based on the above information, answer the following questions.
(i) Measure of angle ADF is equal to
(ii) Measure of angle ACB is equal to
(iii) Width of the river is
OR
Height of the other temple is

Ronit is the captain of his school football team. He has decided to use a 4-4-2-1 formation in the next match. The igure below shows the positions of the players in a 4-4-2-1 formation on a
coordinate grid.One square box represents 1 square unit.
(i)What is the distance between the two centre forward positions in Ronit’s plan?
(ii)What is the area (in square units) of the football field enclosed by the lines joining the two centre back positions and the goalkeeper’s position?
OR
A ball hit from the left full back position travels uninterrupted to the right centre forward
position. What can be the minimum distance traveled by the all?
(iii)Which two positions are on the line x+5y-5=0= 0?

Rahul is driving a car. On his way, he approaches a tall building and observes that Rajesh is
standing at the top of that building. A signboard beside the building read - Angle of depression =60°. The distance from the building at which Rahul stops his car is 50cm.

(i) Is the angle of elevation from Rahul's car to the top of building, where Rajesh is standing the same as the angle of depression ?
(ii) What is the length of the line of sight ?
OR
What is the height of the tower ?
(iii) Will the angle of elevation increase or decrease as the car approaches the building ?

A hunter found a tall tower inside a dense forest. He was planning to climb the tower and noticed that the angle of depression was 40° and the height of the tower was 45 cm. His fellow colleague however, said that the angle of depression is actually 10° less than what the hunter has measured.Keeping into account the new angle of depression, answer the following questions.

(i) What is the new angle of elevation to the top of the tower ?
(ii) What is the new distance of the hunter from the base of the tower ?
OR
If his fellow colleague said that the angle the angle of depression is actually 20° more than
what the hunter has measured, what should be the distance of the hunter from the base of the tower
(iii)Did the distance of the hunter increase or decrease due to change of angle of depression ?

Chandu sees from a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Read the above information and answer the below questions.

(i) What is the height of the tower?
(ii) Find the area of ∆???
OR
Find the area of ∆???
(iii) What is the length of CD?

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is. The
left-right (horizontal) direction is commonly called X-axis. The up-down (vertical) direction is
commonly called Y-axis. In the above Cartesian Coordinates graph, few points are marked for
reference.

(i) Find the distance between E and F.
(ii)Calculate the midpoint of A and B
OR
What is the midpoint of A and E?
(iii) What is the coordinate of D?

An electrician has to repair an electric fault on a pole of height 5 m. He needs to reach
a point 1.3 m below the top of the pole to undertake the repair work. The ladder is
inclined at an angle of 45° to the horizontal.

Based on the above information, answer the following questions.
(i) What is the length of RB?
(ii) What is the distance between the foot of the pole and the foot of the ladder?
(iii) What is the length of the ladder ?
OR
What is the measure of ∠ LRB?

Teewan, Arun and Pankaj were celebrating the festival of Diwali in open ground with
firecrackers. There is a pedestal in the ground. All of sudden Teewan stands on
pedestal and release sky lantern from the top of pedestal.

Based on the above information, answer the following questions.
(i) If the position of Pankaj is 25 m away from the base of pedestal and Zr = 30°, then
find the height of pedestal.
(ii) If the height of pedestal is 30 m, t = 45° and z = 30°, then the horizontal distance
between Arun and Pankaj is
(iii) If the vertical height of sky lantern from the top of pedestal is 12 m and ∠y =
30°, then distance between Teewan and sky lantern is
OR
If ∠q=60° and position of Arun is 15 m away from the base of pedestal, then find the
height of pedestal.

Two hoardings are put on two poles of equal heights standing on either side of the
road. From a point between them on the road the angle of elevation of the top of poles
are 60° and 30° respectively. Height of the each pole is 20 m.

Based on the above information, answer the following questions. (Take √3=1.73).
(i) Find the length of PO.
(ii) Find the length of RO.
(iii) The width of the road is
OR
If the angle of elevation made by pole PQ is 45°, then the length of PO =

A boy is standing on the top of light house. He observed that boat P and
boat Q are approaching to light house from opposite directions. He finds
that angle of depression of boat P is 45° and angle of depression of boat
Q is 30°. He also knows that height of the light house is 100 m.

Based on the above information, answer the following questions.
(i)what is the value of angle ACD ?
(ii) what is the length of CD?
OR
(iii)if angle YAB 30°, then angle ABD is also 30° , why?

The Class X students of a secondary school in Krishinagar have been allotted a rectangular
plot of land for their gardening activity. Sapling of Gulmohar is planted on the boundary of the
plot at a distance of 1 m from each other. There is a triangular grassy lawn inside the plot as
shown in Fig. The students have to sow seeds of flowering plants on the remaining area of
the plot.

(i) Considering A as the origin, what are the coordinates of A?
(ii) What are the coordinates of P?
(iii) What are the coordinates of R?
OR
(iv) What are the coordinates of D?

There are two windows in a house. First window is at the height of 2 m above the
ground and other window is 4 m vertically above the lower window. Ankit and Radha
are sitting inside the two windows at points G and F respectively. At an instant, the
angles of elevation of a balloon from these windows are observed to be 60° and 30° as
shown below-

Based on the above information, answer the following questions.
(i) Who is more closer to the balloon, Radha or Ankit?
(ii) Value of DF is equal to
(iii) Value of h is
OR
Height of the balloon from the ground is

A boy is standing on the top of light house. He observed that boat P and boat Q are
approaching to light house from opposite directions. He finds that angle of depression
of boat P is 45° and angle of depression of boat Qis 30°. He also knows that height of
the light house is 100 m.

Based on the above information, answer the following questions.
(i) If ∠YAB=30°, then ∠ABD is also 30", Why?
(ii)Length of CD is equal to
(iii)Length of BD is equal to
OR
Length of AC is equal to.

An electrician has to repair an electric fault on the pole of height of 8 m. He needs to
reach a point 2 m below the top of the pole to undertake the repair work.

Based on the above information, answer the following questions.
(i) Length of BD is
(ii) What should be the length of ladder, so that it makes an angle of 60° with the
ground?
(iii)What will be the measure of angle BCD when BD and CD are equal?
OR
Find the measure of angle DBC.

A contractor plans to install two slides for the children to play in a park. For the children below theage of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at anangle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a heightof 3m, and inclined at an angle of 60° to the ground. Read the above information and answer the below questions.
(i) Draw a neat labelled figure to show the above situation diagrammatically.
(ii) What is the length of the slide for below 5 years??
OR
What is the length of the slide for elders children?
(iii) Find the time taken for the elder children to slide down if there speed is 5 m/s.