Phoebe and Holden are on opposite sides of a tall tree, 125 m apart. the angles of elevation from each top of the tree are 47 degrees and 36 degrees. what is the height of the tree?
My Answer:
The top angle will be = 180 - (47 + 36) = 97°
then we use the sine law:
(height of tree / sin 47) = (Base / sin 97)
height of tree = (125 x sin 47) / sin 97 = 92.1 m
or is this the answer:
tan 47 = h/x
tan 36 = h/(125-x)
x*tan47 = 125*tan36-x*tan36
x = 125*tan36/[tan47+tan36]
x = 50.485 m
h = 54.138 m
ooblek has not been on line since about 8:30, so I will answer
Your second solution is correct
Your answer using the sine law is invalid since you did not stay within the same triangle
You could have done this:
Let the top of the tree be T
PT/sin36 = 125/sin97
PT = 125sin36/sin97 = 74.0249..
now to the small right-angled triangle ....
sin 47 = h/PT
h = PTsin47 = 54.138, just like the answer to your second method
thanks Reiny
Both answers are correct, and they use different approaches to solve the problem.
Approach 1:
In this approach, the angles of elevation are used to calculate the height of the tree using the sine law. First, we find the top angle by subtracting the sum of the two given angles from 180 degrees (since the three angles of a triangle add up to 180 degrees). Then, we set up the sine law equation, where the height of the tree is the unknown variable. By rearranging the equation and plugging in the values, we can solve for the height.
Approach 2:
In this approach, the tangent of the angles of elevation is used to set up two equations. The unknown variables in the equations are the height of the tree and the distance from Phoebe to the tree. By solving this system of equations, we can find the values of the height and the distance. This approach provides an alternative way to solve the problem.
Both approaches are valid and will give you the correct answer. The choice of which one to use depends on your preference or the method you find easier to understand and apply.