Final answer:
To calculate the height of the tree with a 32-degree angle of elevation from 29 meters away, we use the tangent function of trigonometry. By solving tan(32 degrees) = tree height / 29 m, we find that the tree height is approximately 18.12 meters.
Step-by-step explanation:
To calculate the height of the tree given the angle of elevation and the distance from the tree, we need to use trigonometry, specifically the tangent function. The angle of elevation is 32 degrees and the distance from the observer to the base of the tree is 29 meters. The tangent of an angle in a right-angled triangle represents the ratio of the opposite side to the adjacent side.
The tangent function (tan) of the angle 32 degrees is equal to the height of the tree (opposite side) divided by the distance from the tree (adjacent side), which is 29 meters.
Using the formula:
tan(angle) = opposite/adjacent, we can find:
tan(32 degrees) = tree height / 29 m
Now we solve for the tree height:
tree height = 29 m * tan(32 degrees)
Using a calculator to find tan(32 degrees), we get:
tree height = 29 m * 0.6249
tree height = 18.12 m (rounded to two decimal places)
Therefore, the height of the tree is approximately 18.12 meters.