select whether the law of sines or the law of cosines should be used as the first step in solving the following triangle. then solve the triangle. round your answers to one decimal place. enter the degree symbol by typing deg.

the first step in solving the triangle is to use the dropdown

(m\angle a)

(m\angle b)

(m\angle c)

Question

select whether the law of sines or the law of cosines should be used as the first step in solving the following triangle. then solve the triangle. round your answers to one decimal place. enter the degree symbol by typing deg.

the first step in solving the triangle is to use the dropdown

(m\angle a)

(m\angle b)

(m\angle c)

the first step in solving the triangle is to use the dropdown

(m\angle a)

(m\angle b)

(m\angle c)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Ley de Cosenos", "Ley de Senos" ], "new_concepts": [], "current_concepts": [ "Ley de Cosenos", "Ley de Senos", "Resolución de triángulos oblicuángulos" ] } ## Identificar el primer paso para resolver el triángulo Using the *Ley de Cosenos* knowledge point $$ \begin{aligned} &\text{Lados dados: } a = 11\text{ in (opuesto a } A\text{)}, \quad b = 12\text{ in (opuesto a } B\text{)}, \quad c = 14\text{ in (opuesto a } C\text{)}\ &\text{Caso: Lado-Lado-Lado (LLL)}\ &\text{Método inicial: Ley de Cosenos} \end{aligned} $$ ## Calcular la medida del ángulo A Using the *Ley de Cosenos* knowledge point $$ \begin{aligned} &a^2 = b^2 + c^2 - 2bc \cos(A)\ &11^2 = 12^2 + 14^2 - 2(12)(14) \cos(A)\ &121 = 144 + 196 - 336 \cos(A)\ &121 = 340 - 336 \cos(A)\ &-219 = -336 \cos(A)\ &\cos(A) = \frac{219}{336} \approx 0.651786\ &A = \arccos(0.651786) \approx 49.32^\circ \approx 49.3\text{ deg} \end{aligned} $$ ## Calcular la medida del ángulo B Using the *Ley de Senos* knowledge point $$ \begin{aligned} &\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\ &\sin(B) = \frac{b \cdot \sin(A)}{a}\ &\sin(B) = \frac{12 \cdot \sin(49.3248^\circ)}{11}\ &\sin(B) \approx \frac{12 \cdot 0.75841}{11} \approx 0.827357\ &B = \arcsin(0.827357) \approx 55.82^\circ \approx 55.8\text{ deg} \end{aligned} $$ ## Calcular la medida del ángulo C Using the *Resolución de triángulos oblicuángulos* knowledge point $$ \begin{aligned} &C = 180^\circ - A - B\ &C \approx 180^\circ - 49.3248^\circ - 55.8225^\circ\ &C \approx 74.8527^\circ \approx 74.9\text{ deg} \end{aligned} $$ The first step in solving the triangle is to use the Law of Cosines $m\angle A$ = 49.3 deg $m\angle B$ = 55.8 deg $m\angle C$ = 74.9 deg { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Law of Cosines" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identificar el primer paso para resolver el triángulo

Calcular la medida del ángulo A

Calcular la medida del ángulo B

Calcular la medida del ángulo C

Answer: