Page 7 - 11-Math-12 Application of Trigonometry

112. .QAupapdlircaattiiconEoqfuTartiigoonnsometry eeLLeeaarrnn..PPuunnjjaabb

Now= m∠O 60=andOB 200m

Suppose AB = x meters
In right ∆OAB,

x= sin 6=0 =3 1.732
200 2 2

⇒ x = 200 1.732  = 100(1.732)= 173.2
2 

Hence the height of the kite above the ground = 173.2 m.

Example 2: A surveyor stands on the top of 240 m high hill by the side of a lake. He observes
two boats at the angles of depression of measures 17° and 10°. If the boats are in the same
straight line with the foot of the hill just below the observer, find the distance between the
two boats, if they are on the same side of the hill.

Solution: Let T be the top of the hill TM , where the observer is stationed, A and B be the
positions of the two boats so that m∠XTB = 10° and m∠XTA = 17° and TM = 240m :

( ) Now, m∠MAT =m∠XTA =17 TX MA
( ) and m∠MBT = m∠XTB =10 TX MA

From the figure, TM = tan17
AM

version: 1.1

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