Today in class we learned about how you can estimate heights and distances by using similar triangles. For instance, there is a telephone pole with a shadow of 5 ft. (length) There is a stick next to the telephone pole with a shadow of 1.25 ft. (length) The height of the stick is 2.5 ft. How tall is the telephone pole? the shadow next to the telephone pole makes a right triangle. The shadow next to the stick makes a right triangle. Because the sun is hitting the stick and the telephone pole at the same angle, the two triangles are similar. The telephone pole is 20 ft tall. I figured that out by finding the scale factor of the two triangles. Since I already have corresponding side measures and the height of the small triangle, I can figure it out. The corresponding side measures are 10 ft and 1.25 ft. To find the scale factor, I divided 10 by 1.25. That comes out to 8. Now I know that the scale factor from the smaller triangle to the larger
triangle is 8. To find the height of the telephone pole, I have to use the height of the smaller triangle. The height of the smaller triangle is 2.5 feet. I multiplied the height of the smaller triangle, (2.5 ft) by the scale factor (8). That equals 20 ft. That is the height of the telephone pole.