Question

geometry - unit #8
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name kirsten h
id:
pythagorean theorem solve for missing side
date jan 15/26
period
find the missing side of each triangle. round your answers to three digits as necessary.
1)
3 km
2.5 km
x
2)
12 mi
8 mi
x
3)
9 m
9 m
x
4)
10 mi
6 mi
x
5)
4 cm
13 cm
x
6)
15 mi
9 mi
x

Explanation:

Step1: Recall Pythagorean Theorem

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

Step1: Identify sides, set up formula

$3^2 + x^2 = 25^2$

Step2: Isolate $x^2$

$x^2 = 25^2 - 3^2 = 625 - 9 = 616$

Step3: Solve for $x$

$x = \sqrt{616} \approx 24.820$
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Problem 2

Step1: Identify sides, set up formula

$x^2 = 12^2 + 8^2$

Step2: Calculate $x^2$

$x^2 = 144 + 64 = 208$

Step3: Solve for $x$

$x = \sqrt{208} \approx 14.422$
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Problem 3

Step1: Identify sides, set up formula

$9^2 + 9^2 = x^2$

Step2: Calculate $x^2$

$x^2 = 81 + 81 = 162$

Step3: Solve for $x$

$x = \sqrt{162} \approx 12.728$
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Problem 4

Step1: Identify sides, set up formula

$x^2 + 6^2 = 10^2$

Step2: Isolate $x^2$

$x^2 = 100 - 36 = 64$

Step3: Solve for $x$

$x = \sqrt{64} = 8$
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Problem 5

Step1: Identify sides, set up formula

$4^2 + x^2 = 13^2$

Step2: Isolate $x^2$

$x^2 = 169 - 16 = 153$

Step3: Solve for $x$

$x = \sqrt{153} \approx 12.369$
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Problem 6

Step1: Identify sides, set up formula

$15^2 + 9^2 = x^2$

Step2: Calculate $x^2$

$x^2 = 225 + 81 = 306$

Step3: Solve for $x$

$x = \sqrt{306} \approx 17.493$

Answer:

1. $x \approx 24.820$ km
2. $x \approx 14.422$ mi
3. $x \approx 12.728$ m
4. $x = 8$ mi
5. $x \approx 12.369$ cm
6. $x \approx 17.493$ mi