1. LESSON 8.3B: Applications OBJECTIVE: To solve real-life problems using similar triangles/indirect measurement

2. Indirect measurement is _______ __________________________ __________________________ __________________________ __________________________. the measurement of very large objects or of long distances (which are often made indirectly), using similar triangles and proportions Indirect Measurement with Similar Triangles

3. Thales is know as the first Greek scientist, engineer, and mathematician. Legend claims that he was the first to determine the heights of the Egyptian pyramids by examining their shadows made by the sun. He considered three points: the top of the object, the lengths of the shadows, and the bases. The type of indirect measurement which Thales used is called shadow reckoning. He compared his height and shadow and compared it with the shadow of the pyramid.

4. EXAMPLE: Shadow Reckoning CITY PROPERTY A fire hydrant 2.5 feet high casts a 5-foot shadow. How tall is a street light That casts a 26-foot shadow at the same time? Let h represent the height of the street light.

5. EXAMPLE: Indirect Measurement In the figure at the right, ∆ DBA ~ ∆ ECA. Ramon wants to find the distance across the lake.

6. Indirect Measurement with Similar Triangles I ♥ Geometry! Sir William Snyder’s eye is 168 cm above the ground while he is standing 114 cm from the mirror. If the mirror is 570 cm from the flagpole, how tall is the flagpole?

7. FINAL CHECKS FOR UNDERSTANDING. In the following problems, the triangles are similar. 1. How tall is the tree? 2. Find the distance from the park to the house.

8. HOMEWORK