Tyler used indirect measurement to find the height of a telephone pole. He measured the pole's shadow and his own shadow and drew a diagram. He then converted the measurements to inches and set up similar triangles using the property that parallel lines create similar triangles. He set up a proportion using the corresponding sides of the similar triangles and cross-multiplied to solve for the height of the pole. The height of the pole was found to be 345 inches or 28 feet 9 inches.

1. Warm Up
Convert each measurement.
1. 6 ft 3 in. to inches
2. 5 m 38 cm to centimeters
Find the perimeter and area of each
polygon.
3. square with side length 13 cm
4. rectangle with length 5.8 m and width
2.5 m
75 in.
538 cm
P = 52 cm, A =169 cm2
P =16.6 m, A = 14.5 m2
GT Geometry

2. Indirect measurement is any
method that uses
formulas, similar figures, and/or
proportions to measure an
object. The following example
shows one indirect measurement
technique.

3. Whenever dimensions are given in both feet and
inches, you must convert them to either feet or
inches before doing any calculations.
Helpful Hint

4. Tyler wants to find the height of a
telephone pole.

5. Tyler wants to find the height of a
telephone pole. He measured the
pole’s shadow and his own shadow
and then made a diagram. What is the
height h of the pole?

6. Example 1 Continued
Step 1 Convert the measurements to inches.
Step 2 Find similar triangles.
Because the sun’s rays are parallel, A F.
Therefore ∆ABC ~ ∆FGH by AA ~.
AB = 7 ft 8 in. = (7 12) in. + 8 in. = 92 in.
BC = 5 ft 9 in. = (5 12) in. + 9 in. = 69 in.
FG = 38 ft 4 in. = (38 12) in. + 4 in. = 460 in.

7. Example 1 Continued
Step 3 Find h.
The height h of the pole is 345
inches, or 28 feet 9 inches.
Corr. sides are proportional.
Substitute 69 for BC, h for GH,
92 for AB, and 460 for FG.
Cross Products Prop.92h = 69 460
Divide both sides by 92.h = 345

9. Volume ratios

10. The lateral areas of two similar
cylinders are 50 cm2 and 18
cm2. The volume of the smaller
cylinder is 54 cm3. Find the
volume of the larger cylinder