Un topógrafo usa un instrumento llamado teodolito para medir el ángulo de elevación entre el nivel del piso y la cumbre de una montaña. En un punto, se mide un ángulo de elevación de 41°. Medio kilómetro más lejos de la base de la montaña, el ángulo de elevación medido es de 37°. ¿Qué altura tiene la montaña?

Answers

Answer 1

Answer:

La altura de la montaña es 2848,80 m.

Step-by-step explanation:

Un topógrafo usa un instrumento llamado teodolito para medir el ángulo de elevación entre el nivel del piso y la cumbre de una montaña. En un punto, se mide un ángulo de elevación de 41°.

La función trigonométrica tangente  se define como:

[tex]tan (angulo)=\frac{cateto opuesto}{cateto adyacente}[/tex]

Entonces, siendo h altura de la montaña  e y la distancia de la base de montaña a donde se realiza la medición, la distancia de esta primera observación del topógrafo entre el nivel del piso y la cumbre de una montaña es:

[tex]tan (41)=\frac{h}{x}[/tex]  Ecuación (A)

Medio kilómetro más lejos de la base de la montaña, el ángulo de elevación medido es de 37°. Entonces:

[tex]tan (37)=\frac{h}{x+500m}[/tex]  Ecuación (B)

Entonces, despejando h de la ecuación (A):

h= tan(41)* x

Reemplazando la expresión en la ecuación (B):

[tex]tan (37)=\frac{tan(41)*x}{x+500m}[/tex]

Resolviendo:

tan(37)*(x+500)=  tan(41)* x

0,754*( X +500) = 0,869*X

0,754*X + 377 = 0,869*X

377= 0,869*X -0,754*X

377= 0,115*x

377÷0.115= x

x= 3278,26 m

Entonces, reemplazando en la expresión h= tan(41)* x:

h= tan(41)* 3278,26 m

Resolviendo:

h = 0,869 *3278.26 m  

h = 2848,80 m

La altura de la montaña es 2848,80 m.

En la imagen adjunta se puede observar una representación gráfica de las medidas utilizadas en el problema.

Un Topgrafo Usa Un Instrumento Llamado Teodolito Para Medir El Ngulo De Elevacin Entre El Nivel Del Piso

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Click on the Pic I sent you with the answer to your question hopefully my answer helps you out I tried my best to solve it for you

The interest earned on a $30,000 deposit for six months at 1.5% interest compounded continuously will be $225.846.

What is compound interest?

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

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veggie sticks                    6

chips                                14

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d) percentage of water:

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Step-by-step explanation:

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