A hunter 1.6m tall ,views a bird on top of a tree at an angle 45°. If the distance between the hunter and the tree is 10.4m, find the height of the tree .
To find the height of the tree, we can use the tangent function in trigonometry.
Let's denote the height of the tree as h. When the hunter views the bird at an angle of 45°, a right triangle is formed between the hunter, the tree, and the vertical line from the bird to the ground.
The opposite side of the triangle is the height of the tree (h), and the adjacent side is the distance between the hunter and the tree (10.4m).
Using the tangent function, we have:
tan(45°) = opposite/adjacent
tan(45°) = h/10.4m
Since tan(45°) is equal to 1, we can simplify the equation to:
1 = h/10.4m
To solve for h, we multiply both sides of the equation by 10.4m:
h = 10.4m
Therefore, the height of the tree is 10.4 meters.