SOLUTION: I really appreciate if you could please help me with this problem. You are standing in a meadow near a mountain. The angle of elevation to the top of the mountain is 22 degrees

Algebra ->  Geometry-proofs -> SOLUTION: I really appreciate if you could please help me with this problem. You are standing in a meadow near a mountain. The angle of elevation to the top of the mountain is 22 degrees      Log On


   

Question 119437: I really appreciate if you could please help me with this problem.
You are standing in a meadow near a mountain. The angle of elevation to the top of the mountain is 22 degrees. You move 100 m closer to the mountain and measure the angle of elevation to be 30 degrees. Complete the diagram and determine the height of the mountain, to the nearest meter.
Thank you in advance for your time.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the height of the mountain and the distance to the mountain form a right angle

the height divided by the distance is the tangent of the angle of elevation of the mountain top

let x="height of the mountain" __ x/d=tan(22°) __ x/(tan(22°))=d

x/(d-100)=tan(30°) __ x/(tan(30°))=d-100

x/(tan(30°))=(x/(tan(22°)))-100 __ (x/(tan(30°)))-(x/(tan(22°)))=-100

x(tan(22°))-x(tan(30°))=-100(tan(22°))(tan(30°)) __ x=(-100(tan(22°))(tan(30°)))/((tan(22°))-(tan(30°)))