Siddharth and Ryan used indirect measurement and similar triangles to calculate the height of a soccer net. They measured their own heights and shadow lengths, as well as the shadow length of the net. By setting up proportions between the triangles formed, they were able to calculate the height of the net, which they determined to be approximately 270.9 cm. Their measurement may not be exact due to changes in shadow lengths throughout the day as the sun's position changes.

1. Siddharth Tirumala
Ryan Christianson
B4 Math

2.  Our goal was to find out the height of the
soccer net.
 We did this by using indirect measurement.

3.  Height of:
oRyan: 174 cm
oSiddharth: 158 cm
 Length of:
oRyan’s Shadow: 100 cm
oSiddharth’s Shadow: 90 cm
 Length of Soccer Net’s Shadow: 155 cm

4. This is a picture of the scenario:
Height (Ryan: 174 cm) Siddharth: 158 cm
(Side of soccer net)
Shadow (155 cm) Shadow (Ryan: 174 cm Siddharth: 158 cm)

5.  Similar: Corresponding angles are equal in
measure
 The triangles that were formed in the last
slide are similar

6.  Triangles are similar because their corresponding
angles are equal in measure
 We know this because:
oThere is a right angle, which we know is 90
degrees
oAlso, since the light was coming at the same angle
for both us and the soccer net, the top angles
must be equal in measure.
oSo, if two angles in two triangles are equal to each
other, then the third angles must also be equal
oTherefore, the triangles are similar

7.  Since we knew that the triangles were similar, we
could set up a proportion:
oWe did it for both of our heights.
Using Ryan’s height:
Using Siddharth’s height:

8.  We got different answers for each of us, so
we found the average between the two
answers
 We got 270.9 cm as our answer
 So, the height of the soccer net is
approximately 270.9 cm.

9.  We may not be 100 percent exact on the
measurements
 The length of the shadow changes throughout the
day because it depends on where the sun is in the
sky.
oSo if we had taken the measurements later or
earlier in the day, the lengths of the shadows
may have been different.