A tree stands vertically on a hill side which makes an angle of 15 degree with the horizontal. From a point on the ground 35 meter down the hill from the base of the tree, the angle of elevation of the top of the tree is 60 degree. find the height of the tree.
35¡Ì2 lol
Grinned
I donot know the answer and wants to know
To find the height of the tree, we can use trigonometry. Let's break down the problem step by step:
Step 1: Draw a diagram:
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Ground Tree
We are given:
- Angle A = 15 degrees (angle of the hillside with the horizontal)
- Angle B = 60 degrees (angle of elevation from the point on the ground to the top of the tree)
- Distance CD = 35 meters (distance down the hill from the base of the tree)
We need to find:
- Height of the tree (h)
Step 2: Identify the relevant trigonometric ratios:
We can see that angle B and angle A are related as complementary angles. Therefore, we can apply the tangent ratio:
tangent of angle B = opposite / adjacent
Step 3: Apply the tangent ratio to find the height of the tree:
tangent(60 degrees) = h / 35 meters
tan(60) = h / 35
We know the value of the tangent of 60 degrees is √3. Hence:
√3 = h / 35
Step 4: Solve for the height of the tree:
To isolate h, we can multiply both sides of the equation by 35:
h = √3 * 35
Simplifying:
h = 35√3
So, the height of the tree is 35√3 meters.