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=(d* tan\phi* tan\theta)/(tan\phi-tan\theta)`

Explanation;

In ABC=

`Tan\theta=(y)/(x)`

`x=(y)/(tan\theta)`

In ADC

`Tan\phi=(y)/(x-d)`

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

`y=(d* tan\phi* tan\theta)/(tan\phi-tan\theta)`

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

`y=(d* tan\phi* tan\theta)/(tan\phi-tan\theta)`