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Answer:
132 feet
Step-by-step explanation:
Given that Alejandro is standing at a distance of 140 feet from the base of the tree and his eyes are 6 feet above the ground.
Let AB is the height of the tree and point E is the location of his eyes which is 6 feet above from C on the ground as shown in the figure.
The distance between points A and C, AC=140 feet.
Drawing a horizontal line from point E which meets AB at point D as shown.
As ACED forms a rectangle, so
AC=DE=140 feet ...(i)
CE=AD= 6 feet ...(ii)
The height of the tree, AB=AD+DB
By using equation (ii), AB=6+DB ...(iii)
Now, given that the on watching the top of the tree, the reading on the clinometer is 42 degrees.
So,
In triangle DEB,
[from (i)]
feet
From equation (iii) the height of the tree is
AB=6+126=132 feet.
Hence, the height of the tree is 132 feet.