EN LA CIMA DE UN FARO DE 7 m DE ALTO SE OBSERVA UNA LANCHA CON UN ANGULO DE DEPRESIÓN DE 12 GRADOS. CALCULAR LA DISTANCIA ENTRE LA LANCHA Y EL PIE DEL FARO
Answers
Answer:
33 metros
Step-by-step explanation:
Esto puede simplemente asimilarse a un problema de trigonometria simple. El Vemos un faro con una altura de 7 m, observando una lancha a 12°. Se pide calcular la distancia de la lancha al faro, pero desde su base.
En este caso, necesitamos determinar ese lado. Observando la figura adjunta, podrás notar que solamente debemos calcular el cateto adyacente del triangulo formado entre el faro y la lancha y sus distancias. Para hacer eso, solo usamos la siguiente función trigonométrica:
tgθ = cat op / cat ady (1)
De ahí despejamos el cat ady:
cat ady = cat op / tgθ
Reemplazando tenemos:
cat ady = 7 / tg12
cat ady = 32.93 m o solo 33 m.
Espero te sirva
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance between the boat and the lighthouse is 32.93 meters.
What is Tangent (Tanθ)?
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
Base is the adjacent smaller side of the angle θ.
Como se da que la altura del faro es de 7 m mientras que el ángulo de depresión es de 12°, por tanto, el ángulo entre el barco y la parte superior del faro también es de 12°.
Ahora, la función tangente de la trigonometría se puede escribir como,
[tex]Tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\Tan(12^o) = \dfrac{7\ m}{\text{Distancia entre el faro y el barco}}\\\\\\{\text{Distancia entre el faro y el barco}} = \dfrac{7\ m}{Tan(12^o)}\\\\\\{\text{Distancia entre el faro y el barco}} =32.93\rm\ m[/tex]
Por tanto, la distancia entre el barco y el faro es de 32.93 metros.
In English,
The question is AT THE TOP OF A 7 m HIGH LIGHTHOUSE, A BOAT IS SEEN WITH AN ANGLE OF DEPRESSION OF 12 DEGREES. CALCULATE THE DISTANCE BETWEEN THE BOAT AND THE FOOT OF THE LIGHTHOUSE.
As it is given that the height of the lighthouse is 7 m while the angle of depression is 12°, therefore, the angle between the boat and the top of the lighthouse is also 12°.
Now, the tangent function of the Trigonometry can be written as,
[tex]Tan(\theta)=\dfrac{Perpendicular}{Base}\\\\\\Tan(12^o) = \dfrac{7\ m}{\text{Distance between the light house and the boat}}\\\\\\{\text{Distance between the light house and the boat}} = \dfrac{7\ m}{Tan(12^o)}\\\\\\{\text{Distance between the light house and the boat}} =32.93\rm\ m[/tex]
Hence, the distance between the boat and the lighthouse is 32.93 meters.
Learn more about Tangent (Tanθ):
https://brainly.com/question/10623976
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