Question

finding a missing side using the pythagorean theorem
use the diagrams to find the missing sides of the right triangles.
figure a
?
5.5
4.4
? =
figure d
4.1
?
12.65
? =
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Explanation:

Figure A

Step1: Recall Pythagorean Theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=5.5$, $b=4.4$, solve for $a$.
Rearrange: $a^2 = c^2 - b^2$

Step2: Substitute known values

$a^2 = 5.5^2 - 4.4^2 = 30.25 - 19.36 = 10.89$

Step3: Calculate square root

$a = \sqrt{10.89} = 3.3$

Figure D

Step1: Recall Pythagorean Theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=12.65$, $b=4.1$, solve for $a$.
Rearrange: $a^2 = c^2 - b^2$

Step2: Substitute known values

$a^2 = 12.65^2 - 4.1^2 = 160.0225 - 16.81 = 143.2125$

Step3: Calculate square root

$a = \sqrt{143.2125} = 11.97$ (rounded to two decimals)

Answer:

Figure A: $3.3$
Figure D: $11.97$