SOLUTION: Find the angle of elevation from the point on the ground 90 feet from the base of a building that is 200 feet tall

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Question 625045: Find the angle of elevation from the point on the ground 90 feet from the base of a building that is 200 feet tall
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
It might help to have a diagram.
  • Draw a right triangle with horizontal and vertical legs.
  • The horizontal leg is the ground. Label its length as 90.
  • The vertical leg is the building. Label its length as 200.
  • This makes the angle between the horizontal and the hypotenuse the angle of elevation. Let's label it A.
To solve this problem we need to choose a Trig function whose ratio would include the two sides we know. Since the 90 is adjacent to angle A and the 200 is opposite to angle A, we want to use a ratio that involves adjacent and opposite. So we should use either tan or cot. Since your calculator probably does not have a cot button, we'll use tan:
tan%28A%29+=+200%2F90
Angle A is a acute angle (since it has to fit in a right triangle). And its tan ratio is 200/90. To find A we will use the inverse tan function:
tan%5E%28-1%29%28tan%28A%29%29+=+tan%5E%28-1%29%28200%2F90%29
Using our calculator on the right side we get:
A = 65.77225468
So the angle of elevation is approximately 66 degrees.