Example Question - shadow length
Here are examples of questions we've helped users solve.
Calculating Height of Post Using Similar Triangles
Para resolver esta pregunta, podemos usar las proporciones dictadas por los triángulos semejantes formados por el poste, su sombra y los rayos de luz que llegan al suelo, y la varilla, su sombra y los rayos de luz que llegan al suelo. Dado que tenemos la sombra y la altura de la varilla, podemos establecer la misma relación con el poste y su sombra. La relación es la siguiente: Altura de la varilla / Longitud de la sombra de la varilla = Altura del poste / Longitud de la sombra del poste Sustituyendo los valores que tenemos obtenemos: 49 cm / 63 cm = Altura del poste / 4.5 m Primero, debemos convertir la sombra del poste de metros a centímetros para que las unidades sean consistentes: 4.5 m = 450 cm Ahora, podemos resolver para la altura del poste: 49 cm / 63 cm = Altura del poste / 450 cm (49 cm * 450 cm) / 63 cm = Altura del poste Calculamos el valor numérico: (49 * 450) / 63 = Altura del poste 22050 / 63 = Altura del poste 350 = Altura del poste Por lo tanto, la altura del poste es de 350 cm. Para expresar este valor en metros, dividimos por 100 ya que hay 100 cm en un metro: 350 cm / 100 = 3.5 m Por lo tanto, la altura del poste es de 3,5 metros. La respuesta correcta es la opción a) 3,5 m.
Solving a Right Triangle Problem with Trigonometry
This question involves using trigonometry to solve a right triangle problem. The information provided indicates that Franklin casts a 60° shadow, and the distance from the top of Franklin's head to the shadow's end is 7 feet. The question asks for the length of Franklin's shadow and his height. The 60° angle and the distance from Franklin's head to the shadow's end form a right triangle, with the 7 feet representing the hypotenuse. Let's denote the following: - \( h \) as Franklin's height, - \( s \) as the length of the shadow, - \( 60° \) as the angle of elevation from the end of the shadow to the top of Franklin's head. We can use trigonometry to solve for both \( s \) and \( h \). More specifically, the cosine and sine functions for a 60° angle in a right triangle. Using the cosine function, which is adjacent over hypotenuse: \[ \cos(60°) = \frac{s}{7} \] Since \( \cos(60°) = 0.5 \): \[ 0.5 = \frac{s}{7} \] \[ s = 7 \times 0.5 \] \[ s = 3.5 \text{ feet} \] Using the sine function, which is opposite over hypotenuse: \[ \sin(60°) = \frac{h}{7} \] Since \( \sin(60°) = \sqrt{3}/2 \) or approximately 0.8660: \[ 0.8660 = \frac{h}{7} \] \[ h = 7 \times 0.8660 \] \[ h \approx 6.0620 \text{ feet} \] Rounded to one decimal place, Franklin's height would be approximately 6.1 feet. So, the length of Franklin's shadow is 3.5 feet, and his height is approximately 6.1 feet. The correct answer from the options provided would be: A. 3.5 ft., 6.1 ft.
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