Question

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fluency

1. solve for the missing side of each right triangle below using the pythagorean theorem. if the side length is not an integer, express it in simplest radical form.

(a)
(b)
(c)
(d)

Explanation:

Step1: Aplicar Teorema de Pitágoras (a)

El teorema es $c = \sqrt{a^2 + b^2}$, donde $a=10$, $b=24$.
$\sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676}$

Step2: Calcular la raíz (a)

$\sqrt{676} = 26$

Step3: Aplicar Teorema de Pitágoras (b)

El teorema es $b = \sqrt{c^2 - a^2}$, donde $c=25$, $a=15$.
$\sqrt{25^2 - 15^2} = \sqrt{625 - 225} = \sqrt{400}$

Step4: Calcular la raíz (b)

$\sqrt{400} = 20$

Step5: Aplicar Teorema de Pitágoras (c)

El teorema es $c = \sqrt{a^2 + b^2}$, donde $a=6$, $b=4$.
$\sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52}$

Step6: Simplificar la raíz (c)

$\sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}$

Step7: Aplicar Teorema de Pitágoras (d)

El teorema es $a = \sqrt{c^2 - b^2}$, donde $c=14$, $b=7$.
$\sqrt{14^2 - 7^2} = \sqrt{196 - 49} = \sqrt{147}$

Step8: Simplificar la raíz (d)

$\sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}$

Answer:

(a) 26
(b) 20
(c) $2\sqrt{13}$
(d) $7\sqrt{3}$