pre cal question

Question

To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32°. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 34°. Estimate the height of the mountain. (Round your answer to the nearest foot.)

Answer 1

Cool problem

Draw a triangle with the mountain on the left and label the base as point a and the top as point b. point c is the horizontal distance from the base We are given that angle c is 32 degrees. AB is the side opposite which is the height of the mountain; will label this as o and AC is the adjacent which will label as x

So Tan 32= o/x

Now create a second triangle with the adjacent side 1000 feet closer And label this point as d.

Angle d is 34 degrees and the distance AD is x-1000 (it is 1000 feet closer)

So Tan 34 = o/(x-1000)

Now use your algebra to solve both equations for o

o= x(tan32) and o= (x-1000)(tan34) we have 2 expressions equal to o so they must be equal,to each other(making progress still have a bunch of algebra to do)

x(tan32)= (x-1000)(tan34) distribute

x(tan32)= x(tan34) -1000tan(34). subtract xtan34 from both sides

x(tan32)-x(tan34)= -1000tan(34). Factor out x

x(tan32-tan34)=-1000tan(34). divide both sides by (tan32-tan34)

x= -1000tan34/(tan32-tan34). X=13588 NOT DONE YET

Now can solve for o the height of the mountain

tan32= 0/13588

o=13588(tan32) = 8491 There you go