SOLUTION: When Christine stood south of a mountain, and looked up to the top, the angle of elevation was 21 degrees. When Christine drove 4.5 km closer, she found that the angle of elevation

Algebra ->  Trigonometry-basics -> SOLUTION: When Christine stood south of a mountain, and looked up to the top, the angle of elevation was 21 degrees. When Christine drove 4.5 km closer, she found that the angle of elevation      Log On


   

Question 1187934: When Christine stood south of a mountain, and looked up to the top, the angle of elevation was 21 degrees. When Christine drove 4.5 km closer, she found that the angle of elevation increased by 22 degrees. What is the height of the mountain)
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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When Christine stood south of a mountain, and looked up to the top, the angle of elevation was 21 degrees.
When Christine drove 4.5 km closer, she found that the angle of elevation increased by 22 degrees.
What is the height of the mountain ?
~~~~~~~~~~~~~~~ 


Let h be the mountain height over the roadway level, in kilometers.


Then in the first position, the horizontal distance to the top of the mountain (in x-direction) is  h%2Ftan%2821%5Eo%29 kilometers.


In the second position, the horizontal distance to the top of the mountain (in x-direction) is  h%2Ftan%2843%5Eo%29 kilometers.


Write the difference equation


    h%2Ftan%2821%5Eo%29 - h%2Ftan%2843%5Eo%29 = 4.5 kilometers.


From this equation, express and calculate h


    h = 4.5%2F%281%2Ftan%2821%5Eo%29+-+1%2Ftan%2843%5E0%29%29 = 4.5%2F%281%2F0.3839+-+1%2F0.9325%29 = 2.936 kilometers.    ANSWER


I packed all my calculations in one line, and used an Internet calculator to get values of the tan function of given arguments.

Solved.

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