Asurveyor wishes to determine the height of a mountain. at a given position he measures the angle of elevation to the top as 43.66 degrees. he then moves 1000 feet further from the mountain and measures the angle of elevation to the top as 38.2 degrees. how high is the mountain?

4,486.93 ft

Step-by-step explanation:

Let 'h' be the height of the mountain and 'x' be the horizontal distance between the first position measured and the top of the mountain.

Two right triangles can be modeled such that their tangent relationships yield:

Solving the linear system:

The mountain is 4,486.93 ft high.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.