given that $\triangle abc$ is a right triangle and $ab = 1$, find $ac$, $bc$, $m\angle a$, and $m\angle b$.
enter deg after any value that is in degrees.

$ac$
$ac =$

$bc$
$bc =$

$m\angle a$
$m\angle a =$

$m\angle b$
$m\angle b =$

Question

given that $\triangle abc$ is a right triangle and $ab = 1$, find $ac$, $bc$, $m\angle a$, and $m\angle b$.
enter deg after any value that is in degrees.

$ac$
$ac =$

$bc$
$bc =$

$m\angle a$
$m\angle a =$

$m\angle b$
$m\angle b =$

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Teorema de Pitágoras", "Propiedades del triángulo isósceles", "Triángulos rectángulos especiales" ], "new_concepts": [], "current_concepts": [ "Teorema de Pitágoras", "Propiedades del triángulo isósceles", "Triángulos rectángulos especiales" ] } ## Identificar las propiedades del triángulo $$ \begin{aligned} &\triangle ABC \text{ es un triángulo rectángulo en } C \text{ con marcas de congruencia en } AC \text{ y } BC.\ &AC = BC = x\ &AB = 1 \end{aligned} $$ ## Calcular las longitudes de los lados AC y BC $$ \begin{aligned} &x^2 + x^2 = 1^2\ &2x^2 = 1\ &x^2 = \frac{1}{2}\ &x = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \end{aligned} $$ ## Determinar las medidas de los ángulos $$ \begin{aligned} &\text{Dado que } AC = BC, \text{ el triángulo es isósceles.}\ &m\angle A = m\angle B = \frac{180^\circ - 90^\circ}{2} = 45^\circ \end{aligned} $$ ## Question 1 $AC =$ $\frac{\sqrt{2}}{2}$ ## Question 2 $BC =$ $\frac{\sqrt{2}}{2}$ ## Question 3 $m\angle A =$ $45\text{ deg}$ ## Question 4 $m\angle B =$ $45\text{ deg}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identificar las propiedades del triángulo

Calcular las longitudes de los lados AC y BC

Determinar las medidas de los ángulos

Answer:

Question 1

Question 2

Question 3

Question 4