Final answer:
a) The height of the tree is approximately 80 feet. b) The second observer must look up at an angle of elevation to see the top of the tree.
Step-by-step explanation:
a) How tall is the tree, to the nearest foot?
To find the height of the tree, we can use trigonometry. We have a right triangle formed by the tree, the distance from the first observer to the tree, and the angle of elevation. We can use the tangent function to calculate the height of the tree. Tangent(tan) of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
Tan(angle of elevation) = height of tree / distance from first observer to tree
height of tree = Tan(angle of elevation) * distance from first observer to tree
Using the given values, the height of the tree is approximately 80 feet to the nearest foot.
b) At what angle of elevation must the second observer look up to see the top of the tree?
To find the angle of elevation for the second observer, we can use the same trigonometric approach. We have another right triangle formed by the tree, the distance from the second observer to the tree, and the desired angle of elevation. Again, we can use the tangent function to determine the angle.
Let x be the angle of elevation for the second observer.
Tan(x) = height of tree / distance from the second observer to tree
Using the given values, we can plug them into the equation to find the angle of elevation for the second observer.