Bell Work Find the measure of the missing value in the pair of similar polygons. (Shapes not drawn to scale.) 1. x 30 m 7 m 70 m 3 m 2. 2 mm x 5 mm 27.5 mm 11 m

Indirect Measurement Indirect measurement allows you to use properties of similar polygons to find distances

What is the height of the tree?

You try: Find the length of the flag pole 20 feet

Triangles in the Real World Do you know how tall your school building is? There is an easy way to find out using right triangles. To do this create two similar triangles using the building, its shadow, a smaller object with a known height (like a yardstick), and its shadow. The two shadows can be measured, and you know the height of the yard stick. So you can set up similar triangles and solve for the height of the building. The right angles are equal, and the angles the shadow makes with the ground can assumed to be equal. They can be assumed to be equal because for objects close in distance the sun is the same angle from the ground. Thus the shadows have similar angles, so the triangles are similar. Also the hypotenuses do not matter in these triangles. You could solve for them using Pathagorean’s Theorem, but it isn’t required to solve the problem so we will leave them alone.

Solving for the Building’s Height Here is a sample calculation for the height of a building: building x ft 3 ft = 48 ft 4 ft x feet 48 feet 4x = 144 x = 36 yardstick 3 feet The height of the building is 36 feet. 4 feet

Draw a picture!

Practice: Indirect Measurement Worksheet Day 1