## 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.

1. Michele_Laino

the situation of your problem is like below: |dw:1440317834837:dw|

2. Michele_Laino

then 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

3. anonymous

So I'd make both equations equal to each other, which I understand, but why would I need to solve for a?

4. anonymous

Never mind, I figured it out! Thank you!

5. Michele_Laino

from 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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