A child lies on the ground and looks up at the top of a 17-ft tree nearby. The child is 14 ft away from the tree. What is the angle of elevation from the child to the top of the tree? Round to the nearest whole degree.

Question

anonymous · Answer

So for this problem, we can use trig ratios and a right triangle, since the child is looking to the top of a tree, one of the legs will be the distance between the tree and the child, and the other the height of the tree.  Do you know your trig ratios?

anonymous · Answer

opp/hyp=sin  adj/hyp=cosine and opp/adj=tangent

anonymous · Answer

Good.  So now for the triangle.|dw:1410546652064:dw|

anonymous · Answer

Since we already have the length of two legs, we need only find the value of one of the trig functions for the angle at the bottom left (should have labeled that).  So which trig function uses both of the legs?

anonymous · Answer

tangent

anonymous · Answer

So solve for that function and we'll move to the next step.

anonymous · Answer

tangent is 14/17?

anonymous · Answer

Close, the tangent is the opposite side over the adjacent side so 17/14.

Using a bit of algebra after deriving the ratio, we find that tan(x) = 17/14, the tangent of the angle is the ratio.  We need to find the angle corresponding to the tangent value.  Consequently, we would solve for the atan of 17/14.  This value is 50.52, meaning that the angle of elevation is approximately 51 degrees.

anonymous · Answer

Does it make sense?

anonymous · Answer

yes thank very much

anonymous · Answer

No problem.