From a point on level ground 40m away the angle of elevation of the top of a tree is 32.5m Calculate the height of the tree
Let h be the height of the tree. Then we can use the tangent function to write:
tan(32.5) = h/40
Multiplying both sides by 40, we get:
h = 40*tan(32.5)
Using a calculator, we find:
h ≈ 23.3 m
Therefore, the height of the tree is approximately 23.3 meters.
To calculate the height of the tree, we can use the tangent function and the given angle of elevation. The tangent of an angle is equal to the opposite side divided by the adjacent side.
Let's label the height of the tree as "h" and the distance from the point on the ground to the tree as "x." We can form a right triangle using these values, with the height of the tree representing the opposite side of the angle and the distance representing the adjacent side of the angle.
Using the tangent function, we have:
tan(angle) = opposite / adjacent
tan(32.5°) = h / 40
To find the value of h, we can rearrange the equation:
h = tan(32.5°) * 40
Calculating this expression:
h ≈ 0.656 * 40
h ≈ 26.24 meters
Therefore, the height of the tree is approximately 26.24 meters.