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Activities in Math : Trigonometry


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1.

You are stationed at a radar base and you observe an unidentified plane at an altitude h = 3000 m flying towards your radar base at an angle of elevation = 30o. After exactly one minute, your radar sweep reveals that the plane is now at an angle of elevation = 60o maintaining the same altitude. What is the speed (in m/s) of the plane?
 

2.

A ship of height h = 12 m is sighted from a lighthouse. From the top of the lighthouse, the angle of depression to the top of the mast and the base of the ship equal 30o and 45o respectively. How far is the ship from the lighthouse (in meters)?
 

3.

A pole of height h = 30 ft has a shadow of length l = 17.32 ft at a particular instant of time. Find the angle of elevation (in degrees) of the sun at this point of time.
 

4.

A man is walking along a straight road. He notices the top of a tower subtending an angle A = 60o with the ground at the point where he is standing. If the height of the tower is h = 40 m, then what is the distance (in meters) of the man from the tower?
 

5.

Two men on opposite sides of a TV tower of height 22 m notice the angle of elevation of the top of this tower to be 45o and 60o respectively. Find the distance (in meters) between the two men.
 

6.

Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30o and 60o respectively. If the height of the building is known to be h =90 m, find the distance (in meters) between the two men.
 

7.

Two towers face each other separated by a distance d = 25 m. As seen from the top of the first tower, the angle of depression of the second tower's base is 60o and that of the top is 30o. What is the height (in meters) of the second tower?
 


 
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Related Link(s)
  • Trigonometry Module 3 : Word Problems on Heights and Distances
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