Aperson stands 35.0 m from a flag pole. with a protractor at eye level, he finds that the angle to the top of the flag pole is 25.0 degrees. how high is the flag pole? (the distance from his feet to his eyes is 1.7 m.)

height of flag pole is 18.02 m

Explanation:

given data

distance x = 35 m

angle = 25 degree

eye height y = 1.7 m

to find out

how high is flag ( h)

solution

we will apply here triangle law that is

tanθ = (h - y) / x    1

now we put all these value in equation 1

we get

tanθ = (h - y) / x

tan25 = (h - 1.7) / 35

0.46630 =  (h - 1.7) / 35

h - 1.7 = 0.46630 × 35

h = 16.32 + 1.7

h = 18.02

so height of pole is 18.02 m

18m

Diagrammatically represent the information as follows;

                            E

                            /|

                        /    |

                    /        |

                /            |

        B  /)25°         |C

           |                 |

1.7m     |                 |

        A |                 |D

                  35.0m

As shown in the figure above;

AB represents the distance from his feet to his eyes = 1.7m

AD represents the distance from his feet to the foot of the flag pole = 35.0m

∠EBC represents the angle from his eyes to the top of the flag pole = 25.0°

ED is the height of the flag pole.

To get the height (ED) of the flag pole;

(i) First calculate EC  using the tangent trigonometric function as follows;

tan θ = opposite / adjacent     (i)

Where;

θ = ∠EBC = 25.0°

opposite = EC

adjacent = BC = AD = 35.0m

Substituting these values into equation (i) gives;

tan 25.0°  = EC / 35.0

0.4663 = EC / 35.0

Solve for EC;

EC = 0.4663 x 35.0

EC = 16.3m

(ii) Then, add EC and CD to give ED (which is the height of the pole).

i.e

ED = EC + CD   (where CD = AB = 1.7m)

ED = 16.3 + 1.7

ED = 18m

Therefore the height of the flag pole is 18m

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