http://www.ck12.org Chapter 7. Similarity
7.5 Indirect Measurement
Here you’ll learn how to apply your knowledge of similar triangles and proportions to model real-life situations and
to find unknown measurements indirectly.
What if you wanted to measure the height of a flagpole using your friend George? He is 6 feet tall and his shadow
is 10 feet long. At the same time, the shadow of the flagpole was 85 feet long. How tall is the flagpole? After
completing this Concept, you’ll be able to use indirect measurement to help you answer this question.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter7IndirectMeasurementA
MEDIA
Click image to the left for more content.James Sousa:Indirect MeasurmentUsing Similar Triangles
Guidance
An application of similar triangles is to measure lengths indirectly.
Example A
A tree outside Ellie’s building casts a 125 foot shadow. At the same time of day, Ellie casts a 5.5 foot shadow. If
Ellie is 4 feet 10 inches tall, how tall is the tree?
Draw a picture. From the picture to the right, we see that the tree and Ellie are parallel, therefore the two triangles
are similar to each other. Write a proportion.
4 f t, 10 in
x f t=
5. 5 f t
125 f tNotice that our measurements are not all in the same units. Change both numerators to inches and then we can cross
multiply.