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anonymous
 one year ago
Okay, so my teacher never went over any of the questions on my homework. Fortunately, I was able to figure out just about everything else but this question. Could someone help me out here?
A woman stands at a horizontal distance x from a mountain and measures the angle of elevation of the mountaintop above the horizontal as θ. After walking a distance d closer to the mountain on level ground, she finds the angle to be ϕ. Find a general equation for the height y of the mountain in terms of d, ϕ, and θ, neglecting the height of her eyes above the ground.
anonymous
 one year ago
Okay, so my teacher never went over any of the questions on my homework. Fortunately, I was able to figure out just about everything else but this question. Could someone help me out here? A woman stands at a horizontal distance x from a mountain and measures the angle of elevation of the mountaintop above the horizontal as θ. After walking a distance d closer to the mountain on level ground, she finds the angle to be ϕ. Find a general equation for the height y of the mountain in terms of d, ϕ, and θ, neglecting the height of her eyes above the ground.

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the situation of your problem is like below: dw:1440317834837:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then we can write the subsequent system: \[\Large \left\{ \begin{gathered} H = \left( {d + a} \right)\tan \theta \hfill \\ H = a\tan \phi \hfill \\ \end{gathered} \right.\] which can be solved for a and H, please try to solve that system

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I'd make both equations equal to each other, which I understand, but why would I need to solve for a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Never mind, I figured it out! Thank you!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1from second equation, I get: \[\Large a = \frac{H}{{\tan \phi }}\] substituting into first equation, I can write this: \[\Large H = d\tan \theta + \frac{H}{{\tan \phi }}\tan \theta \] and that last equation can be solved with respect to H
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