Answer:
The height of the tree is approximately 21.4 feet
Step-by-step explanation:
We list out the question parameters first as follows;
The distance from the base of the tree where the angle of elevation is measured, d = 10 feet
The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°
Let 'h' represent the height of the tree, then we have;
The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg
By trigonometric ratio, we have;
∴ h = d × tan(θ)
Plugging in the given values, we get;
h = 10 feet × tan(65°) = 21 feet inches
∴ By rounding to the nearest tenth of a foot, the height of the tree, h ≈ 21.4 feet.