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.