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# Applications of Trigonometry

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From a point P on the ground the angle of elevation of the top of a tower is 30°and tht of the top of a flagstaff fixed on top of the tower is 60°. If the length of the flagstaff is 5m, find the height of tower.

SARAHann  Mar 10, 2017

#2
+4686
+17

The angle between the tower and the hypotenuse is 180 - 90 - 30 = 60º

The angle between the hypotenuse of the right triangle and the flagpole is 180 - 60 = 120º.

The angle between the flagpole and the top line is 30º.

Use Law of Sines to find the hypotenuse of the right triangle.

$$\frac{5}{\sin30}=\frac{x}{\sin30} \\~\\ x = 5$$

Then you can find the height of the tower.

sin30 = tower/5

tower = 5sin30

tower = 2.5 m

I did this but I thought it was wrong because the tower was so short, but I'll go ahead and post it now because I drew a picture :)

hectictar  Mar 10, 2017
edited by hectictar  Mar 10, 2017
edited by hectictar  Mar 10, 2017
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#1
+76808
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Call the tower height,  P *tan(30)

And the  tower ht + the height of the flagstaff = P*tan(60)

And the difference between these two = the height of the flagstaff.....so

Ptan(60) - Ptan(30)  = 5

P [tan(60) - tan(30) ] = 5

P = 5 / [ tan (60) - tan(30) ]  = (5/2)sqrt(3)  m

So....the tower ht  = (5/2)sqrt(3)* tan(30)  =  2.5 m.....

Mmmmmm...not much of a tower !!!!

But....it's correct because the height of the tower and the flagstaff = (5/2)sqrt(3)* tan(60) =

7.5 m   !!!

CPhill  Mar 10, 2017
#4
+302
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Ummm... i did'nt understand. what does P stand for in

"Call the tower height,  P *tan(30)"

SARAHann  Mar 11, 2017
#5
+4686
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P is the distance from the bottom of the tower to the point, P, on the ground.

The height of the tower is P * tan30º because:

In every right triangle, tan θ = side opposite / side adjacent .

so

tan 30 = tower / P

P * tan 30 = tower

hectictar  Mar 12, 2017
#2
+4686
+17

The angle between the tower and the hypotenuse is 180 - 90 - 30 = 60º

The angle between the hypotenuse of the right triangle and the flagpole is 180 - 60 = 120º.

The angle between the flagpole and the top line is 30º.

Use Law of Sines to find the hypotenuse of the right triangle.

$$\frac{5}{\sin30}=\frac{x}{\sin30} \\~\\ x = 5$$

Then you can find the height of the tower.

sin30 = tower/5

tower = 5sin30

tower = 2.5 m

I did this but I thought it was wrong because the tower was so short, but I'll go ahead and post it now because I drew a picture :)

hectictar  Mar 10, 2017
edited by hectictar  Mar 10, 2017
edited by hectictar  Mar 10, 2017
#3
+76808
+16

You are correct, hectictar......not much of a tower...even  for Munchkins..!!!!

CPhill  Mar 10, 2017

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