The angle between the ground at the top of a flag pole is 25o when the observer is at point a. the observer walks 10 m directly towards the flag pole to point b and the angle is now 40o. what is the height of the flag pole assume the observers eyes are 2 m above the ground?

12.4967 m

≈  12.5 m

Step-by-step explanation:

From the solution diagram attached, to find /AB/, we apply sine rule:

AB/Sin 140° =AD/Sin 15°

AB = 10/Sin 15° x Sin 140°

     = 24.8372 m

To calculate the height of the pole we will calculate BC first. Using the right angle triangle ∠ABC, we have:

Sin ∅  =  BC/AB

Sin 25° =   BC/ 24.8372

BC = 24.8372 Sin 25°

    =  10.4967 m

The height of the pole =  BC + 2.0

                                      =  10.4967 + 2.0

                                      = 12.4967

                                     ≈  12.5 m