Using Similarity to Find Indirect Measurements

Indirect Measure

How tall is it?

Some objects may be too tall to measure with rulers.

• How can we measure objects like this?

• Let's ask Thales an ancient Greek mathematician, astronomer and pre-Socratic philosopher.

Multiple Choice

How did Thales measure the height of the pyramid?

• he used a giant ruler

• he used similar triangles

• he asked a tour guide

• he took a time machine to 2021 and asked David (David knows everything)

Indirect Measurement

• Similar triangles can be used to indirectly measure the heights of these objects in real life.

Practice

-Sketch this model in your notebook and label the sides accordingly

-Use what you know abour similar figures to create a proportion to find the missing length.

-Write it down! You will need it for the next slide!

Multiple Choice

What is the height of the flagpole?

• 6 ft

• 9 ft

• 12 ft

• 15 ft

Open Ended

Is there another way we could have found the height of the flagpole?

Fill in the Blanks

Multiple Choice

A 4-meter-tall flagpole casts a 6-meter shadow at the same time that a nearby building casts a 24-meter shadow. What is the height of the building?

• 4 m

• 8 m

• 12 m

• 16 m

Multiple Choice

At the same time a 6 foot person casts a 2 foot shadow, a nearby flagpole casts a ten foot shadow. How tall is the flagpole?

• 10 ft

• 30 ft

• 15 ft

• 20 ft

Multiple Choice

A tree is 72 feet tall and has a shadow that is 12 feet long. A nearby tree has a shadow of 5 feet. How tall is the tree?

• 3 ft

• 30 ft

• 35 ft

• 300 ft

Multiple Choice

A home's height is 40 ft. and casts a shadow that is 12 ft. A car in the driveway is 10 ft. high. How long is the car's shadow?

• 3 ft

• 120 ft

• 12 ft

• 1200 ft