+0  
 
+5
140
5
avatar+302 

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

Best Answer 

 #2
avatar+4174 
+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
Sort: 

5+0 Answers

 #1
avatar+75346 
+12

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   !!!

 

 

cool cool cool

CPhill  Mar 10, 2017
 #4
avatar+302 
+5

Ummm... i did'nt understand. what does P stand for in 

"Call the tower height,  P *tan(30)"

SARAHann  Mar 11, 2017
 #5
avatar+4174 
+6

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
avatar+4174 
+17
Best Answer

 

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
avatar+75346 
+16

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

 

 

cool cool cool

CPhill  Mar 10, 2017

24 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details