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Razones Trigonométricas: Nivel 9°

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Razones Trigonométricas: Nivel 9°

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Quiz de aplicaciones de seno, coseno y tangente.

Created by

fquinonezm@unemi.edu.ec
fquinonezm@unemi.edu.ec
Ecuador

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Razones Trigonométricas: Nivel 9°
 

Razones Trigonométricas: Nivel 9°Online version

Quiz de aplicaciones de seno, coseno y tangente.

by fquinonezm@unemi.edu.ec
1

Un árbol proyecta una sombra de 6 m y el ángulo de elevación del sol es 40°. ¿Cuál es la altura del árbol?

2

Desde el suelo se observa la parte superior de un edificio con ángulo de elevación 35°. Si el observador está a 30 m del edificio, ¿Qué altura tiene?

3

Una escalera forma 60° con el suelo y su base está a 2,5 m de la pared. ¿Cuál es la longitud de la escalera?

4

Un avión despega formando 25° con la horizontal. Si recorre 800 m, ¿qué altura está?

5

Una torre tiene 50 m de altura. Desde un punto, el ángulo de elevación hacia la cima es 30°. ¿Qué distancia horizontal hay hasta la torre?

6

Desde la cima de un edificio de 40 m, se observa un carro con ángulo de depresión 35°. ¿Cuál es la distancia a la base?

7

Un globo está a 120 m de altura y el ángulo de elevación es 50°. ¿Qué distancia horizontal los separa?

Explicación

Usa la razón tan(40°) = altura / sombra → altura = 6 × tan(40°) ≈ 5,03 m.

Aplica tan(35°) = altura / 30 → altura = 30 × tan(35°) ≈ 21,0 m.

cos(60°) = 2,5 / hipotenusa → hipotenusa = 2,5 / cos(60°) = 5,0 m.

sen(25°) = altura / 800 → altura = 800 × sen(25°) = 338 m.

tan(30°) = 50 / distancia → distancia = 50 / tan(30°) = 86,6 m.

El ángulo de depresión es igual al ángulo de elevación desde el carro. tan(35°) = 40 / distancia → distancia = 40 / tan(35°) = 57,1 m.

tan(50°) = 120 / distancia → distancia = 120 / tan(50°) = 100,8 m.

 
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