A flagpole casts a shadow 8.5 meters long. if an algebra student 1.6 meters tall casts a shadow 2.0 meters long at the same time and location, how tall is the flagpole

The flagpole stands vertically on the ground. If a line is drawn from the top of the flagpole to the shadow, it forms a right-angled triangle. Similarly, if a line is drawn from the top of the student's head to the tip of this shadow a right-angled triangle is formed. Since it is given that the measures of both the shadows are taken at the same time and location, the angle of depression in both the cases is equal. Therefore, by AA similarity, height of the flagpole / height of the student = length of shadow of the flagpole/length of shadow of the student flagpole height/1.6m = 8.5 m/2.0m flagpole height = (8.5 m x 1.6m) / 2.0 m = 6.8m

Similar triangles, the corresponding sides have the same ratio

let f = height of the flag pole

f/1.6=8.5/2

Cross multiply

2f = 1.6 * 8.5

2f = 1.6 * 8.5

f=13.6/2

f=6.8

the flagpole is 6.8 m tall