Question

find the missing side length of each right triangle to make it correctly through the maze. shade or color your path as you go.
start
a = 11
b = 60
c = ?
a = 8
b = ?
c = 20
a = 9
b = 10
c = ?
a = 10
b = 24
c = ?
a = 25
b = ?
c = 65
a = 7
b = 17
c = ?
a = ?
b = 35
c = 37
a = 6
b = ?
c = 14
a = 22
b = ?
c = 40
a = 16
b = 30
c = ?
a = 24
b = 45
c = ?
finish!

Explanation:

We use the Pythagorean theorem for right triangles: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $a$ and $b$ are the legs. We solve for the missing value at each step and follow the path matching the calculated value.

Step1: Solve for $c$ (Start)

$a=11$, $b=60$. Calculate $c$:
$$c=\sqrt{11^2 + 60^2}=\sqrt{121+3600}=\sqrt{3721}=61$$
Follow the path labeled 61.

Step2: Solve for $b$

$a=8$, $c=20$. Calculate $b$:
$$b=\sqrt{20^2 - 8^2}=\sqrt{400-64}=\sqrt{336}\approx18.3$$
Follow the path labeled 18.3.

Step3: Solve for $c$

$a=9$, $b=10$. Calculate $c$:
$$c=\sqrt{9^2 + 10^2}=\sqrt{81+100}=\sqrt{181}\approx13.5$$
Follow the path labeled 13.5.

Step4: Solve for $a$

$b=35$, $c=37$. Calculate $a$:
$$a=\sqrt{37^2 - 35^2}=\sqrt{1369-1225}=\sqrt{144}=12$$
Follow the path labeled 12.

Step5: Solve for $b$

$a=6$, $c=14$. Calculate $b$:
$$b=\sqrt{14^2 - 6^2}=\sqrt{196-36}=\sqrt{160}\approx12.6$$
Follow the path labeled 12.6.

Step6: Solve for $c$

$a=16$, $b=30$. Calculate $c$:
$$c=\sqrt{16^2 + 30^2}=\sqrt{256+900}=\sqrt{1156}=34$$
Follow the path labeled 34.

Step7: Solve for $b$

$a=22$, $c=40$. Calculate $b$:
$$b=\sqrt{40^2 - 22^2}=\sqrt{1600-484}=\sqrt{1116}\approx33.4$$
Follow the path labeled 33.4.

Step8: Solve for $c$

$a=7$, $b=17$. Calculate $c$:
$$c=\sqrt{7^2 + 17^2}=\sqrt{49+289}=\sqrt{338}\approx18.4$$
Follow the path labeled 18.4.

Step9: Solve for $b$

$a=25$, $c=65$. Calculate $b$:
$$b=\sqrt{65^2 - 25^2}=\sqrt{4225-625}=\sqrt{3600}=60$$
Follow the path labeled 60.

Step10: Final check

The last path is labeled 18, leading to FINISH.

Answer:

The path through the maze (with missing values) is:

1. $c=61$ (from $a=11,b=60$)
2. $b\approx18.3$ (from $a=8,c=20$)
3. $c\approx13.5$ (from $a=9,b=10$)
4. $a=12$ (from $b=35,c=37$)
5. $b\approx12.6$ (from $a=6,c=14$)
6. $c=34$ (from $a=16,b=30$)
7. $b\approx33.4$ (from $a=22,c=40$)
8. $c\approx18.4$ (from $a=7,b=17$)
9. $b=60$ (from $a=25,c=65$)
10. Reaches FINISH via path 18