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**+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

#1**+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 !!!

CPhill
Mar 10, 2017

#2**+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