A tree casts a shadow 4 metre long on the ground, when the angle of elevation of the sun is 45°.find the height of the tree
h/4 = tan45°
Their are two methods to solve this question......
The tree make angle 90 with the ground and elevation angle is 45 therefore by
tan45=height of tree/length of shadow
Height=4. {As tan45=1}
To find the height of the tree, we can use the trigonometric relationship between the angle of elevation, the height of the tree, and the length of the shadow.
Let's denote the height of the tree as 'h'.
In this case, we have an angle of elevation of 45° and a shadow length of 4 meters.
Using the tangent function, we can set up the following equation:
tan(45°) = h/4
Since the tangent of 45° is equal to 1, we can simplify the equation to:
1 = h/4
To solve for 'h', we multiply both sides of the equation by 4:
4 = h
Therefore, the height of the tree is 4 meters.
To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as h.
We are given that the length of the shadow cast by the tree is 4 meters, and the angle of elevation of the sun is 45°.
Since we have a right triangle formed by the tree, the length of its shadow, and the angle of elevation, we can use the tangent function to solve for the height of the tree.
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the tree (h), and the adjacent side is the length of the shadow (4 meters).
So, we can set up the equation:
tan(45°) = h/4
Now, we can solve for h:
h = 4 * tan(45°)
Using a calculator or trigonometric table, we find that tan(45°) is equal to 1.
Therefore, the height of the tree, h, is:
h = 4 * 1
h = 4 meters
Hence, the height of the tree is 4 meters.