3.5 Applications of Similarity
Objective: Students will use their knowledge of similarity to solve real world problems
Two ladders, one 12 feet long the other 20 feet long are leaned up against a wall and make
the same angle with the ground. The shorter ladder reaches 9 feet up the wall. How far will
the longer ladder reach up the wall?
Step 1: Draw picture if not provided
Step 2: Label your picture with given information
A three foot pole in the ground casts a shadow 4.5 feet long. What is the heigh
of a tree which casts a shadow 30 feet long?
Step 1: Draw picture if not provided
Step 4: Set up ratio and solve
Step 2: Label your picture with given information
Step 3: Identify Similar Triangles
Challenge Problem
On level ground, the base of a tree is 20 ft from the bottom of a flagpole with a height of 48 feet. The tree is shorter
than the pole. At a certain time, their shadows end at the same point 60 ft from the base of the flagpole. How tall
is the tree?
Step 1: Draw picture if not provided
Step 2: Label your picture with given information
Step 3: Identify Similar Triangles
Independent Practice
A tree with a height of 4m casts a shadow 15 m long on the ground. How high is another tree
that casts a shadow which is 20 m long?
What is the height of the roof (h)?
The base of a lamppost is 26 ft from a flagpole that is 62­ft feet high. The lamppost is shorter than the
pole. At a certain time, their shadows end at the same point 94 ft from the base of the flagpole.
How tall is the lamppost?