Aptitude

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:

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Question: 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: Option C

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB = tan 30° = 1         AC = AB x 3 = 1003 m.
AC 3
AB = tan 45° = 1         AD = AB = 100 m.
AD
CD = (AC + AD) = (1003 + 100) m
= 100(3 + 1)
= (100 x 2.73) m
= 273 m.

An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

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Question: An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:
[A].

21.6 m

[B].

23.2 m

[C].

24.72 m

[D].

None of these

Answer: Option A

Explanation:

Let AB be the observer and CD be the tower.

Draw BE CD.

Then, CE = AB = 1.6 m,

      BE = AC = 203 m.

DE = tan 30° = 1
BE 3
DE = 203 m = 20 m.
3

CD = CE + DE = (1.6 + 20) m = 21.6 m.

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:

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Question: 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].

2.3 m

[B].

4.6 m

[C].

7.8 m

[D].

9.2 m

Answer: Option D

Explanation:

Let AB be the wall and BC be the ladder.

Then, ACB = 60° and AC = 4.6 m.

AC = cos 60° = 1
BC 2
BC = 2 x AC
= (2 x 4.6) m
= 9.2 m.

From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

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Question: From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:
[A].

149 m

[B].

156 m

[C].

173 m

[D].

200 m

Answer: Option C

Explanation:

Let AB be the tower.

Then, APB = 30° and AB = 100 m.

AB = tan 30° = 1
AP 3
AP = (AB x 3) m
= 1003 m
= (100 x 1.73) m
= 173 m.

The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

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Question:
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

[A].

0.02

[B].

0.2

[C].

0.04

[D].

0.4

Answer: Option C

Explanation:

Given expression = (11.98)2 + (0.02)2 + 11.98 x x.

For the given expression to be a perfect square, we must have

11.98 x x = 2 x 11.98 x 0.02 or x   = 0.04