Question

Two observers are 300 ft apart on opposite sides of a flagpole. The angles of elevation from the observers to the top of the pole are 16degrees and 20degrees. Find the height of the flagpole.

Answer 1

To find the height of the flagpole, we can use the concept of trigonometry and the fact that the two observers are 300 ft apart. Using the tangent function and the given angles of elevation, we can set up equations to solve for the height of the flagpole.

Step-by-step explanation:

To find the height of the flagpole, we can use the concept of trigonometry and the fact that the two observers are 300 ft apart. Let's call the height of the flagpole H.

We can use the tangent function to find H.

We have two right triangles, one for each observer. In the first right triangle, the angle of elevation is 16 degrees and the opposite side is H.

In the second right triangle, the angle of elevation is 20 degrees and the opposite side is H.

Using the tangent function in both cases, we get:

tan(16 degrees) = H / 300 ft and tan(20 degrees) = H / 300 ft

We can solve these equations to find the value of H.

Answer 2

h = 48.077 ft

Step-by-step explanation:

given,

distance between two observer = 300 ft

angle of elevation to top pole = 16° and 20°

height of the flagpole = ?

now,

Let h be the height of the flagpole

Let x be the distance of the pole

`tan 16^0 = (h)/(x)`

`x =(h)/(tan 16^0)`

now,

again applying

`tan 20^0 = (h)/(300-x)`

`300-x=(h)/(tan 20^0)`

`300-3.49 h=2.75 h`

`6.24h = 300`

h = 48.077 ft