Question

pythagorean theorem - missing sides scavenger hunt
directions: start in box a and find the missing side of the right triangle given the leg and
hypotenuse. find the answer in the \previous answer\ box and fill in the units. then solve
that question next. keep track at the bottom of the page.
a leg = 12
hypotenuse = 16
right triangle image
b leg = 8
hypotenuse = 15
right triangle image
previous answer: 12 previous answer: 11.23
c leg = 10
hypotenuse = 26
right triangle image
d
right triangle image with leg 12 and hypotenuse 20
previous answer: 4 previous answer: 12.69
e
right triangle image with leg 8 and hypotenuse 19
f leg = 3
hypotenuse = 5
right triangle image
previous answer: 15.65 previous answer: 10.58
g leg = 5
hypotenuse = 13
right triangle image
h leg = 14
hypotenuse = 21
right triangle image
previous answer: 16 previous answer: 24
a → → → → → → → __ → a

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is hypotenuse, $a,b$ are legs. To find a missing leg: $b = \sqrt{c^2 - a^2}$.

Step2: Solve Box A

Known: $a=12$, $c=16$.
$b = \sqrt{16^2 - 12^2} = \sqrt{256 - 144} = \sqrt{112} \approx 10.58$
Match to box with "Previous Answer: 10.58" → Box F.

Step3: Solve Box F

Known: $a=3$, $c=5$.
$b = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$
Match to box with "Previous Answer: 4" → Box C.

Step4: Solve Box C

Known: $a=10$, $c=26$.
$b = \sqrt{26^2 - 10^2} = \sqrt{676 - 100} = \sqrt{576} = 24$
Match to box with "Previous Answer: 24" → Box H.

Step5: Solve Box H

Known: $a=14$, $c=21$.
$b = \sqrt{21^2 - 14^2} = \sqrt{441 - 196} = \sqrt{245} \approx 15.65$
Match to box with "Previous Answer: 15.65" → Box E.

Step6: Solve Box E

Known: $a=8$, $c=19$.
$b = \sqrt{19^2 - 8^2} = \sqrt{361 - 64} = \sqrt{297} \approx 17.23$
Match to box with "Previous Answer: 17.23" → Box B.

Step7: Solve Box B

Known: $a=8$, $c=15$.
$b = \sqrt{15^2 - 8^2} = \sqrt{225 - 64} = \sqrt{161} \approx 12.69$
Match to box with "Previous Answer: 12.69" → Box D.

Step8: Solve Box D

Known: $a=12$, $c=20$.
$b = \sqrt{20^2 - 12^2} = \sqrt{400 - 144} = \sqrt{256} = 16$
Match to box with "Previous Answer: 16" → Box G.

Step9: Solve Box G

Known: $a=5$, $c=13$.
$b = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12$
Match to box with "Previous Answer: 12" → Box A (completes the loop).

Answer:

$A
ightarrow F
ightarrow C
ightarrow H
ightarrow E
ightarrow B
ightarrow D
ightarrow G
ightarrow A$