From a point on level ground, the angle of elevation of the top of a tree is 60°.if the tree is 39m high, how far is its base from p?
39 m / p = tan(60º)
p = 39 m / tan(60º)
To find the distance from the base of the tree to the point P, we need to use trigonometry.
Let's assign variables to the given information:
- The angle of elevation of the top of the tree is θ = 60°.
- The height of the tree is h = 39m.
We can use the tangent function to relate the angle of elevation (θ) to the height of the tree (h) and the distance from the base of the tree to point P (x). The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this case, the height of the tree (h) is the opposite side, and the distance from the base of the tree to point P (x) is the adjacent side. Recall that the tangent function is given by:
tan(θ) = opposite/adjacent
Substituting the known values into the equation, we have:
tan(60°) = h/x
The tangent of 60° is √3. Substituting this value and the given height (h = 39m), we have:
√3 = 39/x
Now we need to solve for x. To isolate x, we can multiply both sides of the equation by x:
x * √3 = 39
Divide both sides of the equation by √3 to solve for x:
x = 39/√3
To simplify further, we can rationalize the denominator by multiplying both the numerator and denominator by √3:
x = (39/√3) * (√3/√3)
x = (39√3) / 3
Therefore, the distance from the base of the tree to point P is approximately 13√3 meters.