A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30º with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60º. What is the distance between the base of the tower and the point P?

A) Data inadequate B) 8 units
C) 12 units D) None of these

Answer:   A) Data inadequate


One of AB, AD and CD must have given.

So, the data is inadequate.


The top and bottom of a tower were seen to be at angles of depression 30° and 60° from the top of a hill of height 100 m. Find the height of the tower ?

A) 42.2 mts B) 33.45 mts
C) 66.6 mts D) 58.78 mts
Answer & Explanation Answer: C) 66.6 mts


ht1488353450.jpg image

From above diagram
AC represents the hill and DE represents the tower

Given that AC = 100 m

angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)

Let DE = h

Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE

tan 60°=AC/CE => √3 = 100/CE =>CE = 100/√3 ----- (1)

tan 30° = AB/BD => 1/√3 = 100−h/BD => BD = 100−h(√3)
∵ BD = CE and Substitute the value of CE from equation 1
100/√3 = 100−h(√3) => h = 66.66 mts

The height of the tower = 66.66 mts.

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2 24

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

A) 21.6 m B) 23.2 m
C) 24.72 m D) None of these
Answer & Explanation Answer: A) 21.6 m



 Draw BE {\color{Black} \bot} CD

Then, CE = AB = 1.6 m,

BE = AC = {\color{Black} 20\sqrt{3}m}


{\color{Black}\Rightarrow DE=\frac{20\sqrt{3}}{\sqrt{3}}m=20m}

{\color{Black}\therefore } CD = CE + DE = (1.6 + 20) m = 21.6 m.

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7 1732

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 30º and 45º 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 & Explanation Answer: C) 273 m


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

{\color{Black} Then,AB=100m, \angle ACB=30^{\circ} and \angle ADB=45^{\circ}}

{\color{Black} \frac{AB}{AC}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}\Rightarrow AC=AB\times \sqrt{3}=100\sqrt{3}m}

{\color{Black} \frac{AB}{AD}=\tan 45^{\circ}=1\Rightarrow AD=AB=100 m}

{\color{Black} \therefore CD=(AC+AD)=(100\sqrt{3}+100)m=100(\sqrt{3}+1)=100\times 2.73=273 m}

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4 1353

Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

A) 6 B) 8
C) 9 D) 10
Answer & Explanation Answer: B) 8


Average speed = total distance / total time

Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours

Average speed = 6/ 0.75 = 8 miles/hour

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7 1065

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 & Explanation Answer: D) 1800


If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.

Answer = 1800 

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