a river is 60 metre wide . a tree of unknown height is one bank.the angle of elevation of the top of the tree from the point exactly opposite to the tree , on the other bank is 30°. find the height of the tree
Tan theta=P/B
Tan 30°=h/60
1/√3=h/60
60/√3=h
60√3/√3*√3=h
60√3/3=h
20*1.732=h
h=34.64 m
To find the height of the tree, we can use trigonometry.
Let's denote the height of the tree as 'h.'
From the given information, we know that the river is 60 meters wide, and the angle of elevation from the point exactly opposite to the tree on the other bank is 30°.
First, we need to find the distance between the tree and the point directly opposite it on the other bank.
This distance can be determined by using the trigonometric relationship between the opposite side, adjacent side, and the angle in a right-angled triangle.
Since the angle of elevation is given as 30°, we can deduce that the angle at the bottom is 90° - 30° = 60°.
Using the trigonometric function tan, we can write:
tan(60°) = h / (opposite side)
tan(60°) = h / (60 meters)
tan(60°) = h / 60
Now, we can solve this equation to find the value of h.
Multiply both sides of the equation by 60:
60 * tan(60°) = h
Using a calculator, evaluate the value of tan(60°):
60 * √3 ≈ 103.92
Therefore, the height of the tree, h, is approximately 103.92 meters.