How Tall Is It?
Brian Cook, Hannah Floyd, Robin Lindgren, Kendall Klumpp
3rd Period
Tuesday, March 8, 2011
Robin
60°
Special Right Triangle
•Having the long leg to get the short leg, it is going
to be the long divided by √3.
•This gives you 22/√3.
•22/√3 × √3/√3 = 22√3/3 which is the short leg.
•The hypotenuse is double the short leg, making it
44√3/3
•Adding the short side to the height of myself from
my feet to my eyes, it is 27.08√3.
5.08 ft
30°
22 ft
Trigonometry
•To get the short leg in the
30-60-90, use the tan30
•Tan30 = x/22
•X ≈ 38.11
•Then add 38.11 to my
height to my eyes.
•The length of the building
to the top of the little
square is approximately
43.19
•Because this is not a special right
triangle, the only other option to
solve for the height of the top of
the square on the wall is to use
trigonometry. This will leave us
with an approximate answer.
Hannah
•To get the length of the “short”
leg, find the tangent of 20°:
Tan20=x/37
x≈12.02
12.0
2
•Once the length of the short leg
has been solved, add that length
to the height of my body from my
eyes down to the ground:
70
°
12.02 + 5.29 ≈ 17.31
ft.
37 ft
20
°
•The height of the square on the
wall to the ground is
approximately 17.31 ft.
5.29 ft
Kendall
45º
11ft
45º
11ft
5.25ft
• With a 45-45-90 triangle,
both of the legs are the
same.
• Since I was 11ft away from
the wall, the distance from
the height of my eyes to the
object is the same as the
distance from me to the
wall.
• Thus, it is 11 feet.
• Then adding the distance
from my eye height to the
object, plus the height of
the rest of my body, one
can find that the height
from the object to the
ground is 16.25 ft.
30-60-90
•The short leg of the triangle was 7 feet so the
hypotenuse, which is double the short leg, is 14
feet
•The long leg of the triangle is the short leg × √3,
so the long leg’s length is 7√3.
•To find the height of the total object, you add the
long leg of the triangle and the height from the
ground to my eyes. 5.17+7√3≈17.29
•Therefore, the height of the object is 17.29.
Brian
30˚
Trigonometry
•To find the long leg of the triangle,
you need to find the tan 60˚.
•tan 60˚= x/7 x= 12.12
•Now add the height from the ground
to my eyes is 5.17. Add that height and
the long of the triangle.
•5.17+12.12≈ 17.29.
•Therefore, the height of the object is
17.29.
7√3
17.29
60˚
7 feet
5.17
feet
Conclusion
The average height of the square on the wall was approximately 23.51 ft.
In this process, the group learned to use clinometers for the first time.
Applying our geometry to real life objects was very helpful. It helped the
group realize how math can be applied to ordinary objects.