^{0} when the boat is 80m from the tower. After 10 seconds, the angle of depression becomes 30^{0}. What is the speed of the boat? (Assume that the boat is running in still water).

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The angle of elevation of a ladder leaning against a wall is 60� and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A.

B.

4.6 m

C.

7.8 m

D.

9.2 m

Answer with explanation

Answer: Option DExplanation

cos 60 = 4.6/X where X is the length of the ladder

X = 4.6/cos 60

= 4.6 divided by 1/2

= 9.2

I checked the answer as follows:

By pythagorean theorem, the ladder is 7.967433… feet off the ground.

Sin 60 = 7.967433/9.2

9.2

Workspace

A.

4√3 units

B.

8 units

C.

12 units

D.

Data inadequate

Answer with explanation

Answer: Option DExplanation

One of AB, AD and CD must have given.

So, the data is inadequate.

Workspace

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30� and 45� respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A.

173 m

B.

200 m

C.

273 m

D.

300 m

Answer with explanation

Answer: Option CExplanation

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.

3.87 meter/sec

D.

0.72 meter/sec

Answer with explanation

Answer: Option AExplanation

Workspace

The Top of a 15 metre high tower makes an angle of elevation of 60 degree with the bottom of an electric pole and angle of elevation of 30 degree with the top of pole. Find the height of the electric pole.

A.

7 metre

B.

8 metre

C.

9 metre

D.

10 metre

Answer with explanation

Answer: Option DExplanation

Workspace

A.

22 Km/Hr

B.

28 Km/Hr

C.

32 Km/Hr

D.

36 Km/Hr

Answer with explanation

Answer: Option CExplanation

Workspace

From a point C on a level ground, the angle of elevation of the top of a tower is 30 degree. If the tower is 100 meter high, find the distance from point C to the foot of the tower.

A.

170 meter

B.

172 meter

C.

173 meter

D.

167 meter

Answer with explanation

Answer: Option CExplanation

Workspace

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A.

276 meter

B.

273 meter

C.

270 meter

D.

263 metre

Answer with explanation

Answer: Option BExplanation

Workspace

A.

40sq.ft.

B.

800sq.ft.

C.

1600sq.ft.

D.

40/ sqrt 2 sq.ft.

Answer with explanation

Answer: Option BExplanation

Tan 60° = 3 = | PQ |

QR |

∴ PQ = 3 QR

Tan 30° = | 1 | = | PQ | = | PQ |

3 | SQ | 80+QR |

∴ 80 + QR = 3 PQ

∴ 80 + QR = 3QR

∴ QR = 40 ft.

If we read carefully, we see that the boy (Point R) and the scarecrow (Point Q) are in diagonally opposite corners.

So QR is a diagonal of the square farm.

Diagonal of square = side x 2

∴ 40 = side x 2

∴ side = 40/2

**∴ Area =** (side)^{2} = (40/2)^{2} = (1600/2) **= 800sq.ft.**

Workspace

Two friends Ajay and Vijay formed sand castles of heights of height 8 cm and 15 cm respectively on the seashore. The distance between the two castles was 24 cm. Find the distance between the tops of two castles.

A.

24.5cm

B.

25cm

C.

31cm

D.

24cm

Answer with explanation

Answer: Option BExplanation

Workspace

When the sun’s altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

A.

140 m

B.

60.6 m

C.

35 m

D.

20.2 m

Answer with explanation

Answer: Option BExplanation

Let AD be the tower, BD be the initial shadow and CD be the final shadow.

Given that BC = 70 m, ABD = 30°, ACD = 60°,

Let CD = x, AD = h

From the right CDA,

tan60°=ADCD√3=hx⋯(eq:1)tan60°=ADCD3=hx⋯(eq:1)

From the right BDA,

tan30°=ADBD1√3=h70+x⋯(eq:2)tan30°=ADBD13=h70+x⋯(eq:2)

eq:1eq:2⇒√3(1√3)=(hx)(h70+x)⇒3=70+xx⇒2x=70⇒x=35eq:1eq:2⇒3(13)=(hx)(h70+x)⇒3=70+xx⇒2x=70⇒x=35

Substituting this value of x in eq:1, we have

√3=h35⇒h=35√3=35×1.73=60.55≈60.6

Workspace

^{0} when the boat is 80m from the tower. After 10 seconds, the angle of depression becomes 30^{0}. What is the speed of the boat? (Assume that the boat is running in still water).

A.

20 m/sec

B.

16 m/sec

C.

10 m/sec

D.

18 m/sec

Answer with explanation

Answer: Option BExplanation

Workspace

A man is standing on the deck of a ship, which is 10m above water level. He observes the angle of elevation of the top of a light house as 60^{0} and the angle of depression of the base of the lighthouse as 30^{0}. Find the height of the light house.

A.

45m

B.

30m

C.

38m

D.

40m

Answer with explanation

Answer: Option DExplanation

Workspace

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