1) a) Picture: A man standing next to a building, both casting shadows on the ground. The man's shadow ends at the same point as the building's shadow.
b) Proportion: (Man's height) / (Man's shadow length) = (Building's height) / (Building's shadow length)
c) Substitute: 6 ft / 11 ft = h / 128 ft
d) Solve: h = (6 * 128) / 11 ≈ 70.09 ft
2) a) Picture: Two trees of different heights casting shadows on the ground. The first tree is 4m tall with a 15m shadow. The second tree has a 20m shadow.
b) Proportion: (First tree height) / (First tree shadow) = (Second tree height) / (Second tree shadow)
c) Substitute: 4 m / 15 m = h / 20 m
d) Solve: h = (4 * 20) / 15 ≈ 5.33 m
3) a) Picture: Roger standing next to a flagpole, both casting shadows on the ground. Roger's shadow ends at the same point as the flagpole's shadow.
b) Proportion: (Roger's height) / (Roger's shadow length) = (Flagpole's height) / (Flagpole's shadow length)
c) Substitute: 5.6 ft / 11 ft = h / 30 ft
d) Solve: h = (5.6 * 30) / 11 ≈ 15.27 ft
4) a) Picture: A truck driving off a cliff, casting a 20ft shadow on the ground below. Simultaneously, a 5ft newspaper stand casts a 4ft shadow.
b) Proportion: (Newspaper stand height) / (Newspaper stand shadow) = (Cliff height) / (Truck's shadow)
c) Substitute: 5 ft / 4 ft = h / 20 ft
d) Solve: h = (5 * 20) / 4 = 25 ft
Parent Tip: Review the logic above to help your child master the concept of similar triangles word problems worksheet.
