Question

finding a missing side using the pythagorean theorem
use the diagrams to find the missing sides of the right triangles.
figure a
?
9.5
7.6
? =
figure d
?
4
10.57
? =

Explanation:

Step1: Define Pythagorean Theorem

For a right triangle with hypotenuse $c$, and legs $a,b$: $a^2 + b^2 = c^2$

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For Figure A:

Step2: Assign values to variables

Let $c=9.5$, $b=7.6$, $a=?$

Step3: Rearrange to solve for $a$

$a = \sqrt{c^2 - b^2}$

Step4: Substitute values and calculate

$a = \sqrt{9.5^2 - 7.6^2} = \sqrt{90.25 - 57.76} = \sqrt{32.49}$

Step5: Compute final value for Figure A

$\sqrt{32.49} = 5.7$

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For Figure D:

Step6: Assign values to variables

Let $c=10.57$, $a=4$, $b=?$

Step7: Rearrange to solve for $b$

$b = \sqrt{c^2 - a^2}$

Step8: Substitute values and calculate

$b = \sqrt{10.57^2 - 4^2} = \sqrt{111.7249 - 16} = \sqrt{95.7249}$

Step9: Compute final value for Figure D

$\sqrt{95.7249} = 9.784$ (rounded to 9.78, or exactly 9.784)

Answer:

Figure A: $5.7$
Figure D: $9.78$ (or $9.784$ for exact value)