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The angle of elevation of the top of a tower from a point on the ground is 30° . On walking 100m towards the tower the angle of elevation changes to 60° . Find the height of the tower.

A.

80√3

B.

70√3

C.

60√3

D.

50√3

Answer with explanation

Answer: Option DExplanation

Workspace

On the same side of a tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 600 m, the distance between the object

A.

254 m

B.

284 m

C.

344 m

D.

384 m

Answer with explanation

Answer: Option AExplanation

Workspace

If an object travels at five feet per second, how many feet does it travel in one hour?

A.

30

B.

3000

C.

18

D.

1800

Answer with explanation

Answer: Option DExplanation

If an object travels at 5 feet per second it covers 5×60 feet in one minute,

and 5x60x60 feet in one hour.

Answer = 1800

Workspace

** **A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

A.

12 cm

B.

8 cm

C.

9.5 cm

D.

7.5 cm

Answer with explanation

Answer: Option BExplanation

Workspace

An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?

A.

381 m

B.

211 m

C.

169 m

D.

254 m

Answer with explanation

Answer: Option AExplanation

Workspace

A balloon leaves the earth at a point A and rises vertically at uniform speed. At the end of 2 minutes, John finds the angular elevation of the balloon as 60°. If the point at which John is standing is 150 m away from point A, what is the speed of the balloon?

A.

0.63 meter/sec

B.

2.16 meter/sec

C.

0.72 meter/sec

D.

3.87 meter/sec

Answer with explanation

Answer: Option BExplanation

Workspace

A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60º. When he moves 50 m away from the bank, he finds the angle of elevation to be 30º.

A.

38.3, 19 m

B.

45.3, 32 m

C.

41.3, 28 m

D.

43.3, 25 m

Answer with explanation

Answer: Option DExplanation

Let AD be the tree of height h,

In ΔADC,

tan60º = h/CD

Or, √3 = h/CD

Or, CD = h/√3

In ΔADB,

tan30º = h/BD

Or, 1/√3 = h/BD

Or, BD = h√3

BD – CD = 50

h√3 – h/√3 = 50

(3h – h)/√3 = 50

2h = 50√3

Height of the tree,

h = 50√3/2

= 25√3 25×1.732

= 43.3 m.

Width of the river,

CD = h/√3

= 25√3/√3

= 25 m.

Workspace

A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder.

A.

4.23m

B.

6.23m

C.

8.25m

D.

7.53m

Answer with explanation

Answer: Option AExplanation

Let AB be the wall and CB, the ladder.

Then, AC = 3m and ∠ACB = 45º

∴ Length of the ladder = CB = 3 √2

= (3 × 1.41) m = 4.23 m

Workspace

A.

170 meter

B.

172 meter

C.

173 meter

D.

167 meter

Answer with explanation

Answer: Option CExplanation

Let AB be the tower.

then∠ACB=30∘AB=100ABAC=tan=>100AC=13–√=>AC=3–√∗100=>AC=1.73∗100=>AC=173metermeter30∘then∠ACB=30∘AB=100meterABAC=tan30∘=>100AC=13=>AC=3∗100=>AC=1.73∗100=>AC=173meter

Please always remember the value of square root 3 is 1.73, and the value of square root 2 is 1.41.

This will be very helpful while solving height and distance questions and saving your time.

Workspace

A.

8.65 m

B.

7.63m

C.

5m

D.

9.5m

Answer with explanation

Answer: Option AExplanation

Let BA be the ladder and AC be the wall as shown above.

Then the distance of the foot of the ladder from the wall = BC

Given that BA = 10 m , BAC = 60°

sin 60°=BCBA√32=BC10BC = 10×√32=5×1.73=8.65 m

Workspace

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