Question

right triangles practice
name:
pythagorean theorem
directions: use the pythagorean theorem to find the missing side of the triangle. set up an equation then solve. show all work on this paper.
1.
2.
3.
4.
5.
6.
$8^{2}+x^{2}=83^{2}$
$64+x^{2}=6889$
$x^{2}=6889-64=6825$
$x=\sqrt{6825}=\sqrt{25×273}=5\sqrt{273}$
$63^{2}+89^{2}=x^{2}$
$3969+7921=x^{2}$
$x^{2}=11890 \\ x=\sqrt{11890}$
$24^{2}+x^{2}=62^{2}$
$576+x^{2}=3844$
$x^{2}=3844-576=3268$
$x=\sqrt{3268}=\sqrt{4×817}=2\sqrt{817}$
$53^{2}+72^{2}=x^{2}$
$2809+5184=x^{2}$
$x^{2}=7993 \\ x=\sqrt{7993}$
$30^{2}+57^{2}=x^{2}$
$900+3249=x^{2}$

Explanation:

Step1: Recall Pythagorean Theorem

For right triangles: $a^2 + b^2 = c^2$, where $c$ = hypotenuse, $a,b$ = legs.
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Problem 1

Step1: Identify sides and set up equation

8 = leg, 63 = hypotenuse, $x$ = missing leg: $8^2 + x^2 = 63^2$

Step2: Calculate squared values

$64 + x^2 = 3969$

Step3: Isolate $x^2$

$x^2 = 3969 - 64 = 3905$

Step4: Solve for $x$

$x = \sqrt{3905} \approx 62.49$
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Problem 2

Step1: Identify sides and set up equation

63,89 = legs, $x$ = hypotenuse: $63^2 + 89^2 = x^2$

Step2: Calculate squared values

$3969 + 7921 = x^2$

Step3: Sum and solve for $x$

$x^2 = 11890$, $x = \sqrt{11890} \approx 109.04$
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Problem 3

Step1: Identify sides and set up equation

24 = leg, 62 = hypotenuse, $x$ = missing leg: $24^2 + x^2 = 62^2$

Step2: Calculate squared values

$576 + x^2 = 3844$

Step3: Isolate $x^2$

$x^2 = 3844 - 576 = 3268$

Step4: Solve for $x$

$x = \sqrt{3268} \approx 57.17$
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Problem 4

Step1: Identify sides and set up equation

53,72 = legs, $x$ = hypotenuse: $53^2 + 72^2 = x^2$

Step2: Calculate squared values

$2809 + 5184 = x^2$

Step3: Sum and solve for $x$

$x^2 = 7993$, $x = \sqrt{7993} \approx 89.40$
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Problem 5

Step1: Identify sides and set up equation

30,57 = legs, $x$ = hypotenuse: $30^2 + 57^2 = x^2$

Step2: Calculate squared values

$900 + 3249 = x^2$

Step3: Sum and solve for $x$

$x^2 = 4149$, $x = \sqrt{4149} \approx 64.41$
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Problem 6

Step1: Identify sides and set up equation

60 = leg, 65 = hypotenuse, $x$ = missing leg: $60^2 + x^2 = 65^2$

Step2: Calculate squared values

$3600 + x^2 = 4225$

Step3: Isolate $x^2$

$x^2 = 4225 - 3600 = 625$

Step4: Solve for $x$

$x = \sqrt{625} = 25$

Answer:

1. $\approx 62.49$
2. $\approx 109.04$
3. $\approx 57.17$
4. $\approx 89.40$
5. $\approx 64.41$
6. $25$