Rs Aggarwal 2019 Solutions for Class 10 Math Chapter 14 Heights And Distances are provided here with simple step-by-step explanations. These solutions for Heights And Distances are extremely popular among Class 10 students for Math Heights And Distances Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 Book of Class 10 Math Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 Solutions. All Rs Aggarwal 2019 Solutions for class Class 10 Math are prepared by experts and are 100% accurate.
Page No 635:
Answer:
Let be the tower standing vertically on the ground and O be the position of the observer.
We now have:
∠ and ∠
Let:
m
Now, in the right ∆, we have:
=
⇒
⇒ =
Hence, the height of the pole is 34.64 m.
Page No 635:
Answer:
Let be the horizontal ground and be the position of the kite.
Also, let O be the position of the observer and be the thread.
Now, draw ⊥ .
We have:
∠, m and ∠
Height of the kite from the ground = = 75 m
Length of the string, m
In the right ∆, we have:
⇒
⇒ m
Hence, the length of the string is m.
Page No 635:
Answer:
Let CE and AD be the heights of the observer and the chimney, respectively.
We have,
So, the height of the chimney is 53.46 m (approx.).
Page No 635:
Answer:
Let the height of the tower be AB.
We have,
So, the height of the tower is 10 m.
Page No 635:
Answer:
Let BC and CD be the heights of the tower and the flagstaff, respectively.
We have,
So, the height of the flagstaff is 87.8 m.
Page No 635:
Answer:
Let BC be the tower and CD be the water tank.
Page No 636:
Answer:
Let AB be the tower and BC be the flagstaff.
We have,
So, the height of the tower is 3 m.
Page No 636:
Answer:
Let be the pedestal and be the statue such that m.
We have:
∠ and ∠
Let:
m and m
In the right ∆, we have:
⇒
⇒
Or,
Now, in the right ∆, we have:
⇒
On putting in the above equation, we get:
⇒
⇒
⇒ m
Hence, the height of the pedestal is 2 m.
Page No 636:
Answer:
Let be the unfinished tower, be the raised tower and O be the point of observation.
We have:
m, ∠ and ∠
Let m such that m.
In ∆AOB, we have:
⇒
⇒ m = m
In ∆, we have:
⇒
⇒ m
∴ Required height = m = 86.6 m
Page No 636:
Answer:
Let be the horizontal plane, be the tower and be the vertical flagpole.
We have:
m, ∠ and ∠
Let:
m and m
In the right ∆, we have:
⇒
⇒ m
Now, in the right ∆, we have:
⇒
⇒
By putting in the above equation, we get:
⇒
⇒
Thus, we have:
Height of the flagpole = 10.4 m
Height of the tower = 5.19 m
Page No 636:
Answer:
Let AB and CD be the equal poles; and BD be the width of the road.
We have,
Hence, the height of each pole is 20 m and point P is at a distance of 20 m from left pole and 60 m from right pole.
Page No 636:
Answer:
Let be the tower and be the positions of the two men standing on the opposite sides. Thus, we have:
∠, ∠ and m
Let m and m such that m.
In the right ∆, we have:
⇒
⇒ m
In the right ∆, we have:
⇒
⇒
On putting in the above equation, we get:
⇒ m
∴ Distance between the two men = m
Page No 636:
Answer:
Let PQ be the tower.
We have,
So, the distance between the cars is 273 m.
Page No 636:
Answer:
Let PQ be the tower.
So, the time taken to reach the foot of the tower from the given point is 3 seconds.
Page No 637:
Answer:
Let PQ=h m be the height of the TV tower and BQ=x m be the width of the canal.
We have,
So, the height of the TV tower is and the width of the canal is 10 m.
Page No 637:
Answer:
Let AB be the building and PQ be the tower.
We have,
So, the height of the building is 20 m.
Page No 637:
Answer:
Let be the first tower and be the second tower.
Now, m and m such that m and ∠.
Let m such that m and m.
In the right ∆, we have:
⇒
⇒
⇒
⇒ = m
∴ Height of the first tower = m
Page No 637:
Answer:
Let PQ be the chimney and AB be the tower.
We have,
So, the height of the chimney is 120 m.
Hence, the height of the chimney meets the pollution norms.
In this question, management of air pollution has been shown.
Page No 637:
Answer:
Let AB be the 7-m high building and CD be the cable tower.
We have,
So, the height of the tower is 19.12 m.
Page No 637:
Answer:
Let PQ be the tower.
We have,
So, the height of the tower is 17.32 m and its distance from the point A is 30 m.
Page No 637:
Answer:
Let PQ be the tower.
We have,
So, the height of the tower is 15 m.
Page No 637:
Answer:
Let AD be the tower and BC be the cliff.
We have,
So, the height of the tower is 43.92 m.
Page No 637:
Answer:
Let be the deck of the ship above the water level and be the cliff.
Now,
m such that m and ∠ and ∠.
If AD = x m and m, then m.
In the right ∆, we have:
⇒
⇒ m
In the right ∆, we have:
⇒
⇒
⇒ [∵ ]
⇒ m
∴ Distance of the cliff from the deck of the ship = m
And,
Height of the cliff = m
Page No 638:
Answer:
We have,
So, the height of the tower PQ is 94.6 m.
Page No 638:
Answer:
Let the height of flying of the aeroplane be PQ = BC and point A be the point of observation.
We have,
So, the speed of the aeroplane is 122 m/s or 439.2 km/h.
Page No 638:
Answer:
Let be the tower.
We have:
m, ∠ and ∠
Let:
m and m
In the right ∆, we have:
⇒
⇒
Now, in the right ∆, we have:
⇒
⇒
On putting in the above equation, we get:
⇒
⇒
⇒ m
Hence, the height of the tower is 129.9 m.
Page No 638:
Answer:
Let be the lighthouse and B and C be the two positions of the ship.
Thus, we have:
m, ∠ and ∠
Let:
m and m
In the right ∆, we have:
⇒
⇒ m
Now, in the right ∆, we have:
⇒
⇒
On putting in the above equation, we get:
m
∴ Distance travelled by the ship during the period of observation = m
Page No 638:
Answer:
Let and be two points on the banks on the opposite side of the river and be the point on the bridge at a height of 2.5 m.
Thus, we have:
m, ∠PAD and ∠
In the right ∆, we have:
⇒
⇒ m
In the right ∆, we have:
⇒
⇒ m
∴ Width of the river = m
Page No 638:
Answer:
Let be the tower and be two points such that m and m.
Let:
m, ∠ and ∠
In the right ∆BCA, we have:
In the right ∆BDA, we have:
Multiplying equations (1) and (2), we get:
Height of a tower cannot be negative.
∴ Height of the tower = 6 m
Page No 638:
Answer:
Let AB and CD be the two opposite walls of the room and the foot of the ladder be fixed at the point O on the ground.
We have,
So, the distance between two walls of the room is 7.24 m.
Page No 638:
Answer:
Let OP be the tower and points A and B be the positions of the cars.
We have,
So, the height of the tower is 236.6 m.
Disclaimer: The answer given in the texbook is incorrect. The same has been rectified above.
Page No 638:
Answer:
Let AC be the pole and BD be the ladder.
We have,
So, he should use 3.46 m long ladder to reach the required position.
Page No 639:
Answer:
We have,
Page No 639:
Answer:
Suppose AB be the tower of height h meters. Let C be the initial position of the car and let after 12 minutes the car be at D. It is given that the angles of depression at C and D are 30º and 45º respectively.
Let the speed of the car be v meter per minute. Then,
CD = distance travelled by the car in 12 minutes
CD = 12v meters
Suppose the car takes t minutes to reach the tower AB from D. Then DA = vt meters.
Substituting the value of h from equation (i) in equation (ii), we get
Page No 639:
Answer:
Let CD be the height of the aeroplane above the river at some instant. Suppose A and B be two points on both banks of the river in opposite directions.
Height of the aeroplane above the river, CD = 300 m
Now,
CAD = ADX = 60º (Alternate angles)
CBD = BDY = 45º (Alternate angles)
In right ∆ACD,
In right ∆BCD,
∴ Width of the river, AB
= BC + AC
Thus, the width of the river is 473 m.
Page No 639:
Answer:
Let BC be the 20 m high building and AB be the communication tower of height h fixed on top of the building. Let D be a point on ground such that CD = x m and angles of elevation made from this point to top and bottom of tower are and .
In
Also, in
Page No 639:
Answer:
Let PQ be the hill of height h km. Let R and S be two consecutive kilometre stones, so the distance between them is 1 km.
Let QR = x km.
From equation (i) and (ii) we get,
Hence, the height of the hill is 1.365 km.
Page No 639:
Answer:
Let AB be the vertically standing pole of height h units and CB be the length of its shadow of s units.
Since, the ratio of length of pole and its shadow at some time of day is given to be
In
Page No 646:
Answer:
Let AB represents the vertical pole and BC represents the shadow on the ground and θ represents angle of elevation the sun.
Hence, the correct answer is option (c).
Page No 646:
Answer:
Here, AO be the pole; BO be its shadow and be the angle of elevation of the sun.
Hence, the correct answer is option (c).
Page No 647:
Answer:
(b) 30°
Let be the pole and be its shadow.
Let and such that (given) and be the angle of elevation.
From ∆, we have:
⇒
⇒
⇒
Hence, the angle of elevation is .
Page No 647:
Answer:
Let AB be the pole, BC be its shadow and be the sun's elevation.
Hence, the correct answer is option (a).
Page No 647:
Answer:
Let AB be a stick and BC be its shadow; and PQ be the tree and QR be its shadow.
We have,
Hence, the correct answer is option (d).
Page No 647:
Answer:
Let AB be the wall and AC be the ladder.
We have,
Hence, the correct answer is option (d).
Page No 647:
Answer:
Let AB be the wall and AC be the ladder.
We have,
Hence, the correct answer is option (c).
Page No 647:
Answer:
Let AB be the tower and point C be the point of observation on the ground.
We have,
Hence, the correct answer is option (b).
Page No 647:
Answer:
Let AB be the tower and point C be the position of the car.
We have,
Hence, the correct answer is option (b).
Page No 647:
Answer:
Let point A be the position of the kite and AC be its string.
We have,
Hence, the correct answer is option (b).
Page No 647:
Answer:
Let AB be the cliff and CD be the tower.
We have,
Hence, the correct answer is option (b).
Disclaimer: The answer given in the textbook is incorrect. The same has been rectified above.
Page No 647:
Answer:
Let AB be the lamp post; CD be the girl and DE be her shadow.
We have,
Hence, the correct answer is option (c).
Page No 648:
Answer:
Let CD = h be the height of the tower.
We have,
Hence, the correct answer is option (d).
Page No 648:
Answer:
Let AB be the rod and BC be its shadow; and be the angle of elevation of the sun.
Hence, the correct answer is option (a).
Page No 648:
Answer:
Let AB be the pole and BC be its shadow.
We have,
Hence, the correct answer is option (b).
Page No 648:
Answer:
Let the sun's altitude be .
We have,
Hence, the correct answer is option (a).
Page No 648:
Answer:
Let AB and CD be the two towers such that AB = x and CD = y.
We have,
Hence, the correct answer is option (c).
Page No 648:
Answer:
(b)
Let be the tower and be the point of observation.
Also,
∠ and m
Let:
m
In ∆, we have:
⇒
⇒ m
Hence, the height of the tower is m.
Page No 648:
Answer:
(a)
Let be the string of the kite and be the horizontal line.
If ⊥ , then m and ∠.
Let:
m
In the right ∆, we have:
⇒
⇒ m
Hence, the height of the kite is m.
Page No 648:
Answer:
(b)
Let be the tower and and be the points of observation on .
Let:
∠, ∠ and m
Thus, we have:
and
Now, in the right ∆ABC, we have:
⇒ ...(i)
In the right ∆ABD, we have:
⇒ ...(ii)
On multiplying (i) and (ii), we have:
⇒ [ ∵ ]
⇒
⇒ m
Hence, the height of the tower is m.
Page No 648:
Answer:
(b)
Let be the tower and and be the points of observation such that ∠, ∠, m and m.
Now, in ∆, we have:
⇒
⇒
In ∆, we have:
⇒
∴
⇒
⇒ ⇒
∴ Height of the tower AB = m
Page No 648:
Answer:
(c)
Let be the rectangle in which ∠ and cm.
In ∆, we have:
⇒
⇒ m
Again,
⇒
⇒ m
∴ Area of the rectangle = cm2
Page No 649:
Answer:
(b)
Let be the hill making angles of depression at points and such that ∠, ∠ and km.
Let:
km and km
In ∆, we have:
⇒ ⇒ ...(i)
In ∆, we have:
⇒ ...(ii)
On putting the value of taken from (i) in (ii), we get:
⇒
⇒
⇒
On multiplying the numerator and denominator of the above equation by , we get:
km
Hence, the height of the hill is km.
Page No 649:
Answer:
(c)
Let be the pole and and be its shadows.
We have:
∠, ∠ and m
In ∆, we have:
⇒ ⇒ m
Now, in ∆, we have:
⇒ ⇒ m
∴ Difference between the lengths of the shadows = m
Page No 649:
Answer:
(b) 30 m
Let be the observer and be the tower.
Draw ⊥ , Let metres. Then,
m , m and ∠.
= m.
In right ∆, we have:
⇒
⇒
⇒ m
Hence the height of the tower is m.
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