Similar Triangles Application

Steps for solving application problems: Read the problem carefully. Draw a diagram to represent the situation if it has not been given. Set up the proportion to solve for the missing length. Solve the proportion. Make sure the answer makes sense and attach any units to the answer.

Example 1 A top of a 30 ft ladder touches the side of a building at 25 feet above the ground. A 12 ft ladder is placed at the same angle against a tree. How far up the tree does the 12 ft ladder reach?

Example 2 A tree cast a 25 ft shadow at the same time that a 3 foot child cast a 10 ft shadow. Find the height of the tree.

Example 3 A person that is 168 cm tall is standing 456 cm from the flagpole cast a shadow that is 114 cm long. The flagpole cast a shadow that is 570 cm long. How tall is the flagpole?

Example 4 Use similar triangles to find the length of the lake. 1.5 mi

Example 5 Most TV screens have similar shapes. The measure of the diagonal is used to give screen size. Suppose the dimensions of an 18 inch screen are 11 inches by 15 inches. Find the dimensions of a 35 in TV.

Example 6 The Jones family planted a tree at the birth of each child. In comparing the heights of the child and the tree, the family determined that when their son was 20 ft from the tree, his shadow and the tree’s shadow coincide. The son is now 6 feet tall and cast a 9 ft shadow. How tall is the tree?

Try This! A tower casts a shadow of 64 feet. A 6 foot tall pole near the tower casts a shadow 8 feet long. How tall is the tower? Draw a picture to illustrate and solve.

Try This! A flagpole cast a shadow 3 meters long. A woman near the pole casts a shadow 0.75 meters long. The woman is 1.5 meters tall. How tall is the flag pole?

Try This! Find the length of the lake. 6 mi 9 mi 15 mi 4 mi 6 mi

Try This! Find the height of the building using similar triangles.