Similar Triangles and Indirect Measurement Lesson

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

LET'S DISCUSS!

Lena is standing on the beach when she sees a tall sailing ship pass by 1,000 meters offshore. She holds a ruler vertically 24 inches in front of her eyes, and the ship appears to be  $\frac{7}{8}$   inch high.  The figure shown represents the situation as two similar right triangles. Find the approximate height (h) of the sailing ship above the water rounded to the nearest tenth.

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