Question

2/11 pythagorean thrm missing sides canvas work
name: zyla sheba22
show your work for each problem, then submit into canvas and turn in the worksheet. you will not get credit for the assignment until the work is turned in.
2.
(the figure is not drawn to scale.)
3.
4.
(the figure is not drawn to scale.)
5.
6.

1. which are pythagorean triples? show work for all 5 sets.

□ 6, 8, 10
□ 8, 10, 12
□ 10, 16, 15
□ 12, 16, 20
□ 14, 18, 20
8.
success criteria:
*label a, b, & c on the triangle (remember: biggest value is c)
*set up the values in the pythagorean theorem for every problem
*show all steps solving the pythagorean theorem

Explanation:

Step1: Find hypotenuse (Q2)

Apply Pythagorean theorem: $c = \sqrt{a^2 + b^2}$
$\sqrt{60^2 + 32^2} = \sqrt{3600 + 1024} = \sqrt{4624}$

Step2: Calculate hypotenuse (Q2)

$\sqrt{4624} = 68$

Step3: Find hypotenuse (Q3)

Apply Pythagorean theorem: $c = \sqrt{7^2 + 24^2}$
$\sqrt{49 + 576} = \sqrt{625}$

Step4: Calculate hypotenuse (Q3)

$\sqrt{625} = 25$

Step5: Find missing leg (Q4)

Apply Pythagorean theorem: $a = \sqrt{c^2 - b^2}$
$\sqrt{4^2 - 3^2} = \sqrt{16 - 9} = \sqrt{7}$

Step6: Calculate missing leg (Q4)

$\sqrt{7} \approx 2.65$ ft

Step7: Find missing leg (Q5)

Apply Pythagorean theorem: $a = \sqrt{c^2 - b^2}$
$\sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144}$

Step8: Calculate missing leg (Q5)

$\sqrt{144} = 12$ in

Step9: Solve for x (Q6)

Apply Pythagorean theorem: $(5x)^2 + (8x+4)^2$ is not needed; use given $x=4$ to verify sides: $5(4)=20$, $8(4)+4=36$, hypotenuse = $\sqrt{20^2+36^2}=\sqrt{400+1296}=\sqrt{1696}=4\sqrt{106}\approx41.18$

Step10: Verify triple 6,8,10 (Q7)

Check $6^2 + 8^2 = 10^2$
$36 + 64 = 100$, $100=100$: valid

Step11: Verify triple 8,10,12 (Q7)

Check $8^2 + 10^2 = 12^2$
$64 + 100 = 164$, $164
eq144$: invalid

Step12: Verify triple 10,16,15 (Q7)

Check $10^2 + 15^2 = 16^2$
$100 + 225 = 325$, $325
eq256$: invalid

Step13: Verify triple 12,16,20 (Q7)

Check $12^2 + 16^2 = 20^2$
$144 + 256 = 400$, $400=400$: valid

Step14: Verify triple 14,18,20 (Q7)

Check $14^2 + 18^2 = 20^2$
$196 + 324 = 520$, $520
eq400$: invalid

Step15: Find missing leg (Q8)

Apply Pythagorean theorem: $a = \sqrt{c^2 - b^2}$
$\sqrt{12.8^2 - 8^2} = \sqrt{163.84 - 64} = \sqrt{99.84}$

Step16: Calculate missing leg (Q8)

$\sqrt{99.84} \approx 9.99$ cm $\approx10.0$ cm

Answer:

1. 68
2. 25
3. $\sqrt{7} \approx 2.65$ ft
4. 12 in
5. Sides: 20, 36, $4\sqrt{106}\approx41.18$
6. Valid Pythagorean Triples:

• 6, 8, 10
• 12, 16, 20

1. $\approx10.0$ cm