Answer to Question #178059 in Geometry for Abdul Abduli

Question

15. A math teacher at Vallivue High School measured the angle of elevation from the ground to the flag at

the top of the school’s flagpole. She took the measurement from the ground 25 feet away from the

flagpole, and found that it was a 50 ◦ angle of elevation. When the flag was lowered to half-staff, she

found the angle decreased by 18 ◦. How much was the flag lowered, in feet? Draw a diagram to

support your answer.

Answer 1

The diagram is given below.

In diagram, A is the flag position, C is the point where the flag is lowered.

AB=25 ft

AC=h ft

BC=x ft

by using trigonometry,

$$tan50\degree=\dfrac{h}{25} \newline h=25tan50\degree$$

And,

$$tan32\degree=\dfrac{h-x}{25} \newline x=h-25tan32\degree\newline x=25tan50\degree-25tan32\degree\newline x=14.17\space ft$$

Thus, the flag lowered by 14.17 ft.