An arborist monitors growth of a baobab tree in an arboretum by standing 8 meters from the base of the tree and measuring the angle of elevation to the top. The angle of elevation to one tree is 30∘.
What is the approximate height of the tree?
Is it 4.6 m ?
it is 13.9 m
To any future answer seekers, Cat's response is absolutely correct. I just took the test and got 13.9 m correctly. I hope this helps!!!
To find the height of the tree, you can use trigonometry and the information provided: the distance from the base of the tree to the observer and the angle of elevation.
Let's assume that the height of the tree is h meters.
Using trigonometry, we can use the tangent function to relate the angle of elevation and the height of the tree:
tan(angle of elevation) = height of tree / distance to tree
In this case, the angle of elevation is 30 degrees and the distance to the tree is 8 meters, so we have:
tan(30 degrees) = h / 8
To find the value of tangent of 30 degrees, we can use a scientific calculator or an online calculator. The tangent of 30 degrees is approximately 0.5774.
Now we can solve for h:
0.5774 = h / 8
Multiply both sides by 8:
8 * 0.5774 = h
h ≈ 4.6192 meters
So the approximate height of the tree is 4.62 meters, not 4.6 meters.