Question

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.

Answer 1

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

Answer 2

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.

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