# 1/26/16- Indirect Measurement

Warm-up

a.) From the diagram above, create a similarity statement and give a reason.

b.) if BA=28, CE=20, and ED=45, find AE.

Indirect Measurement

Shadow Problems– Ex.) A 5ft tall person casts an 8ft shadow, while at the same time, a lightpost casts a 12ft shadow. How tall is the lightpost?

Key ideas to solve this problem: All rays of light that hit a certain part of the earth at the same time, are basically parallel (they’re technically not, but the difference in their angles is unimaginably small). This means that angle of a ray of light with the ground is the same everywhere (in a given area, at the same time) The other idea is that when we know the height of something, that length is always perpendicular to the ground (forms a right angle). These facts give us the following diagram, of two similar triangles (by AA):

Since the two triangles are similar (by AA) we can create a proportion from their corresponding sides: h/12=5/8. From there, we can solve for h and find that h=7.5ft.

Mirror Problems- Ex.) A 5ft tall person sees the top of a building reflected from a mirror on the ground. The mirror is 100ft away from the building and 10 ft away from the person. Find the height of the building.

Key Ideas- When you look at a mirror from an angle (not head on), the image you see is the same angle from the other side of the mirror (I’m trying to say this statement in regular words). A key idea is line of sight. When you look at a mirror, there is a line of sight from your eyes to the mirror. This line of sight creates an angle with the plane that the mirror is on. The thing you are looking at in the mirror could also be thought of as having a line of sight to the mirror. This line of sight needs to create the same angle with the mirror as your line of sight did. The other key idea is once again: Height and ground meet at right angles! This gives us the following diagram:

Once again, the two triangles we see are similar by AA (due to the right angles they both have, and the congruent angles by the properties of reflections in mirrors). This allows us to create a proportion from corresponding sides: 5/10=h/100. After solving, we can see that h=50ft, so the building is 50ft tall.

We then began work on a worksheet, which is due on Friday, January 29th. Indirect Measurement and Triangle Similarity

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