Answer:
14.3 feet
Step-by-step explanation:
Let the height of the tree = x feet.
It is given that the horizontal distance from the base of tree = 10 feet and the angle of elevation to the nest is 55°.
So, we get the following figure.
As, we are obtaining a right angled triangle.
Using the trigonometric form for the angles of a right angled triangle, we get,
\(\tan x=\frac{opposite}{adjacent}\)
i.e. \(\tan 55=\frac{x}{10}\)
i.e. \(x=10\times \tan 55\)
i.e. \(x=10\times 1.43\)
i.e. \(x=14.3\)
Hence, the height of the tree is 14.3 feet.
