Applications of Similarity

Measuring what you cannot reach.

12 problems · about 21 minutes · G-SRT.B.5

What this lesson teaches

The student uses similar triangles to find inaccessible lengths and applies scale drawings.

Straightforward practice. Get the method working first.

5 problems

A 2 m post casts a 3 m shadow. A tower casts a 30 m shadow. Height in metres?
Answer 20
Why 20 m.
At a scale of 1 to 500, what is the ratio of areas?
Answer 1 to 250000, the square of the length ratio.
Why The length ratio is squared.
A 3 m post casts a 4 m shadow. A tree casts a 20 m shadow. Tree height in metres?
Answer 15
Why h ÷ 20 = 3 ÷ 4.
A 2 m post casts a 5 m shadow. A building casts a 40 m shadow. Height in metres?
Answer 16
Why h ÷ 40 = 2 ÷ 5.
Scale 1 to 200. A drawn 5 cm stands for how many centimetres?
Answer 1000
Why 5 × 200.

The same ideas with more to keep track of.

3 problems

Scale 1 to 50. A real 600 cm is drawn as how many centimetres?
Answer 12
Why 600 ÷ 50.
At scale 1 to 100, areas are in what ratio? Enter the second number.
Answer 10000
Why 100 squared.
A 1 m stick casts a 2 m shadow. A pole casts a 14 m shadow. Height in metres?
Answer 7
Why Half the shadow.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Put the shadow method in order.
Answer 1. Note that the sun is at the same angle for both objects. 2. Conclude the two triangles are similar by AA. 3. Set the height to shadow ratios equal. 4. Cross-multiply and solve for the unknown height.
Why Similarity must be established before any ratio is written.
Scale 1 to 25. A real 300 cm is drawn as how many centimetres?
Answer 12
Why 300 ÷ 25.
The Tree: A 2 m post casts a 3 m shadow. A tree casts a 21 m shadow. How tall is the tree, in metres?
Answer 14 m
Why 14 m.
The Map: A map has scale 1 to 500. A drawn length of 4 cm stands for how many centimetres?
Answer 2000
Why 2000 cm, which is 20 m.