SOLUTION: Sandy stops to check on Tom, who is on a ladder recovering a frisbee from the roof. When tom talks to sandy, who is standing 25 feet from the house, the angle of depression is 50 d

Algebra ->  Trigonometry-basics -> SOLUTION: Sandy stops to check on Tom, who is on a ladder recovering a frisbee from the roof. When tom talks to sandy, who is standing 25 feet from the house, the angle of depression is 50 d      Log On


   

Question 717637: Sandy stops to check on Tom, who is on a ladder recovering a frisbee from the roof. When tom talks to sandy, who is standing 25 feet from the house, the angle of depression is 50 degrees. From Sandra perspective, what is the angle of elevation? How far above the ground is Tom?(round to the nearest hundred). How far up the ladder has Tom climbed?(round to the nearest hundred). For safest use of a ladder, the reccomended angle is 75 degrees (as formed by the ladder and the ground). Is Tom using the ladder safely (within 2 degrees of recommendation)? show calculations.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Angles of depression and angles of elevation are both measured from a horizontal. Horizontal lines are parallel. The angle of depression from Tom and the angle of elevation from Sandy are alternate interior angles.(Draw a diagram if you are having trouble seeing this.) Alternate interior angles formed by parallel lines and a transversal are always congruent. So the angle of elevation from Sandy's perspective will be the same as the angle of depression from Tom's perspecitive, 50 degrees.

In the right triangle formed by Tom, Sandy and the point on the ground directly under Tom, we know that the side on the ground is 25 feet and that the angle at Sandy is 50 degrees. Tom's height would be the length of the vertical side from hi to the point on the ground underneath him. Relative to the angle at Sandy, Tom's height would be opposite and the 25 foot side would be adjacent. (Again, a diagram would help.) So we use tan (which is opposite over adjacent):
tan%2850%29+=+x%2F25
Multiplying by 25:
25%2Atan%2850%29+=+x
25%2A1.1917535925942099587053080718604+=+x
29.79383981485524896763270179651+=+x
To the nearest 100th:
29.79+=+x
So Tom is approximately 29.79 feet high.

The rest of the problem cannot be solved. Some piece of information is missing. It could be any of the following:
  • The distance from the bottom of the ladder to Tom.
  • The distance from the house to where the ladder touches the ground.
  • The distance from Sandy to where the ladder touches the ground.
  • The angle formed by the ladder and the house.
  • The angle of depression from Tom to the bottom of the ladder.