For this item, we think of a right triangle with hypotenuse equal to 50 m. Initially, the angle near this angle is equal to 10°. The height of the hill and the horizontal distance from the root of the tree to the point are calculated below,
height of hill, h: sin 15° = h / 50 ; h = 12.94 m
horizontal distance, x: cos 15° = x / 50 ; x = 48.30 m
Then, we solve for the vertical distance from the foot of the hill to the top of the tree by the given angle of elevation.
tan 18° = y / 48.30 m ; y = 15.69 m
We subtract the height of the hill from the value of y in order to determine the height of the tree,
height of the tree = 15.69 m - 12.94 m = 2.75 m
Therefore, the height of the tree is equal to 2.75 m.
