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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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Sansi

Here take this solution in my writing
Hope you understand it....I mean my writing

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Answer:\(y=\frac{d\times tan\phi\times tan\theta}{tan\phi-tan\theta}\)

Explanation;

In ABC=

\(Tan\theta=\frac{y}{x}\)

\(x=\frac{y}{tan\theta}\)

In ADC

\(Tan\phi=\frac{y}{x-d}\)

Using value of x from (1) in (2) , we get:

\(y=\frac{d\times tan\phi\times tan\theta}{tan\phi-tan\theta}\)

General equation for the height y of the mountain in terms of d, ϕ, and θ.

\(y=\frac{d\times tan\phi\times tan\theta}{tan\phi-tan\theta}\)

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